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Differential geometry of submanifolds (Q1133178)

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scientific article; zbMATH DE number 3654968

Language	Label	Description	Also known as
English	Differential geometry of submanifolds	scientific article; zbMATH DE number 3654968

Statements

scholarly article

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Differential geometry of submanifolds (English)

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Journal of Soviet Mathematics

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publication date

1975

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zbMATH Keywords

research survey

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submanifold

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projective space

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affine geometry

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euclidean geometry

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minimal submanifold

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space form

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MaRDI profile type

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2-families of lines in \(P_ 5\) and pairs of congruent lines in \(P_ 3\)

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Complete minimal surfaces in Euclidean \(n\)-spaces

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ISOMETRIC IMMERSIONS OF TWO-DIMENSIONAL RIEMANNIAN METRICS IN EUCLIDEAN SPACE

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Some estimates for almost umbilical surfaces

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Imbedding of pseudo-Riemannian manifolds in a pseudo-Euclidean space

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Reducibility of Euclidean immersions of low codimension

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Three theorems on manifolds with bounded mean curvature

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Vector forms and integral formulas for hypersurfaces in Euclidean space

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On minimal immersions of $S^2$ in $S^{2m}$

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Zur projektiven Differentialgeometrie der Regelflächen im vierdimensionalen Raum

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The fundamental theorems of the theory of surfaces in an afffine space with metric

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The holonomy algebra of immersed manifolds of codimension two

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Hypersurface of an even-dimensional sphere satisfying a certain commutative condition

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Hypersurfaces of odd-dimensional spheres

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On the intrinsic geometry of \(S^n \times S^n\)

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Local estimates for the gradient of non‐parametric surfaces of prescribed mean curvature

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Submanifolds of spheres

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Minimal immersions of surfaces in Euclidean spheres

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Shorter Notes: Spherical Images of Convex Surfaces

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Isometric immersions with semi-definite second quadratic forms

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Immersions of manifolds with non-negative sectional curvatures

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MINIMAL IMMERSIONS OF SPHERES INTO SPHERES

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Representations of compact groups and minimal immersions into spheres

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Minimal immersions of spheres into spheres

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Rigidity and convexity of hypersurfaces in spheres

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A remark on minimal imbedding of surfaces in $E^{4}$

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Surfaces of curvature $łambda_N=0$ in $E^{2+N}$

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On an inequality of mean curvatures of higher degree

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On the Total Curvature of Immersed Manifolds, I: An Inequality of Fenchel-Borsuk-Willmore

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On the mean curvature of submanifolds of euclidean space

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Shorter Notes: Submanifolds in a Euclidean Hypersphere

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On a theorem of Fenchel-Borsuk-Willmore-Chern-Lashof

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Some Integral Formulas for Hyper-Surfaces in Euclidean Spaces

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Minimal Surfaces in S m with Gauss Curvature ≦0

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On an Inequality of Mean Curvature

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Minimal Surfaces with Constant Gauss Curvature

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Surfaces with parallel mean curvature vector

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An integral formula for submanifolds and its application

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On the Total Curvature of Immersed Manifolds, II: Mean Curvature and Length of Second Fundamental Form

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Pseudo-umbilical surfaces with constant Gauss curvature

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Pseudo-umbilical submanifolds of a Riemannian manifold of constant curvature . II

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On a Variational Problem on Hypersurfaces

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A Characterization of Standard Flat Tori

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Surfaces with a parallel isoperimetric section

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G-total curvature of immersed manifolds

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An Invariant of Conformal Mappings

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Rigidity theorems for surfaces in euclidean space

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Surfaces with Mean Curvature Vector Parallel in the Normal Bundle

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Scalar Curvature, Inequality and Submanifold

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On submanifolds of submanifolds of a Riemannian manifold

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Special conformally flat spaces and canal hypersurfaces

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Submanifolds umbilical with respect to a non-parallel normal subbundle

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Conformally Flat Spaces of Codimension 2 in a Euclidean Space

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Pseudo-umbilical submanifolds of codimension $3$ with constant mean curvature

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On Tight Isometric Immersion of Codimension Two

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More on Tight Isometric Immersions of Codimension Two

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On the curvatures of a piece of hypersurface in Euclidean space

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On the isometry of compact submanifolds in Euclidean space

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Minimal Submanifolds of a Sphere with Second Fundamental Form of Constant Length

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On the global isometric embedding of pseudo-Riemannian manifolds

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Characteristic Hypersurfaces in General Relativity. I

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Über einander ein- und umbeschriebene Laplace-Ketten in mehrdimensionalen projektiven Räumen

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Konjugierte Systeme und Kegelschattengrenzen auf Hyperflächen im projektiven \(n\)-dimensionalen Raum

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Zur projektiven Kinematik der Hüllflächen gewisser Hyperquadrikscharen.

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Reduction of the codimension of an isometric immersion

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Isometric Immersions of Constant Mean Curvature and Triviality of the Normal Connection

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Riemannian manifolds of constant curvature and the growth function of submanifolds

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The torsion form of submanifolds in \(E^ N\)

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On isometric immersions between hyperbolic spaces

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Immersionen mit paralleler zweiter Fundamentalform: Beispiele und Nicht- Beispiele

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Non-parametric hypersurfaces with bounded curvatures

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Local theory of affine hypersurfaces

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Remark on Mean Curvature

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The Steiner point of a closed hypersurface

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Remarks on Almgren's interior regularity theorems

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Minimale Untermannigfaltigkeiten von Sphären

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Subscalar pairs of metrics and hypersurfaces with a nondegenerate second fundamental form

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Deformations of normal vector fields and the generalized Minkowski problem

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Metric properties of one parametric systems of linear $k$-dimensional spaces in the Euclidean space $E_n$

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Principal curvature forms

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Almost Complex Submanifolds of the Six Sphere

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Isometric embeddings

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Isometric embeddings of Riemannian and pseudo-Riemannian manifolds.

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Relative Chern-Lashof theorems

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Isoperimetric inequalities for manifolds with boundary

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Rigidity of hypersurfaces of constant scalar curvature

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Riemannsche Mannigfaltigkeiten konstanter positiver Krümmung in euklidischen Räumen der Kodimension 2

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On the Ricci and Weingarten Maps of a Hypersurface

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Surfaces in constant curvature manifolds with parallel mean curvature vector field

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Surfaces of constant mean curvature in manifolds of constant curvature

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Isometric immersions of manifolds with plane geodesics into Euclidean space

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Das Einspannungsproblem 2-dimensionaler Flächen im 5-dimensionalen affinen Raum

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Some immersions in pseudo-Riemannian manifolds of constant curvature

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On an Integral Formula for Closed Hypersurfaces of the Sphere

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Surfaces with Maximal Lipschitz-Killing Curvature in the Direction of Mean Curvature Vector

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Remarks on closed minimal submanifolds in the standard Riemannian m- sphere

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Minimal submanifolds of low cohomogeneity

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Parallel and central transformations of Riemannian manifolds

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Affine Differential Geometry of Closed Hypersurfaces<sup>†</sup>

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Complete surfaces in $E^{4}$ with constant mean curvature

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Minimal surfaces with $M$-index $2$, $T_{1}$-index $2$ and $T_{2}$-index $2$

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Minimal surfaces in $4$-dimensional Riemannian manifolds of constant curvature

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Minimal surfaces in a Riemannian manifold of constant curvature

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On certain hypersurfaces in a real space form

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Isotropic immersions

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Isometric Embedding of a Compact Riemannian Manifold into Euclidean Space

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The monosystems of projective spaces whose asymptotic lines are straight lines

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Monoparametric systems of projective spaces

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Théoreme de Peeling et hypersurfaces isotropes

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Some remarks on minimal submanifolds

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Some results for an orientable 5-dimensional submanifold of \(R^ 7\)

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On tori with parallel mean curvature vector in a space of constant curvature

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On compact minimal surfaces with non-negative Gaussian curvature in a space of constant curvature. I

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On submanifolds in spaces of constant and constant holomorphic curvatures

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Imbeddings of homogeneous spaces with minimum total curvature

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Certain properties of submanifolds in a Riemannian manifold of constant curvature admitting a conformal Killing vector

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Immersions of Riemannian manifolds with a given normal bundle structure. I

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Imbedding of a space with an affine connection in the affine space

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Der Satz von Gauß-Bonnet für Abbildungen in \(E^ N\) und damit verwandte Probleme

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Minimal total absolute curvature for immersions

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Congruence of hypersurfaces

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Some intrinsic characterizations of minimal surfaces

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Über eine Art von Krümmungsinvarianten beliebiger Untermannigfaltigkeiten des \(n\)-dimensionalen euklidischen Raums

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On singularities of surfaces in 𝐸⁴

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On tight immersions of maximal codimension

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Isometric immersions into spaces of constant curvature

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Isometric immersions of Riemannian products

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Isometric immersions of space forms in space forms

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Reducibility of Isometric Immersions

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Certain properties of a submanifold in a sphere

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Compact orientable submanifolds in a Riemannian manifold of constant curvature admitting certain tensor fields

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On a pseudo umbilical submanifold in a Riemannian manifold of constant curvature

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On hypersurfaces which are close to spheres

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An analog of the Hilbert's theorem with constant positive curvature

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An inequality for twodimensional surfaces in fourdimensional space

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On certain integral formulas for hypersurfaces in a constant curvature space

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On hypersurfaces with constant scalar curvature in a Riemannian manifold of constant curvature

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Compact hypersurfaces in an odd dimensional sphere

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On hypersurfaces satisfying a certain condition on the curvature tensor

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A characterization of \(n\)-spheres in space forms and its complex analogue

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Some results in E. Cartan's theory of isoparametric families of hypersurfaces

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On the Gauss mapping for hypersurfaces of constant mean curvature in the sphere

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A formula of Simons' type and hypersurfaces with constant mean curvature

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The Gauss map of immersions of Riemannian manifolds in spaces of constant curvature

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Certain hypersurfaces of an odd dimensional sphere

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Compact orientable submanifold of codemension 2 in an odd dimensional sphere

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Submanifolds and a Pinching Problem on the Second Fundamental Tensors

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Hypersurfaces of \(S^{2n+1} (k)\) in \(E^{2n+2}\)

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A pinching problem on the second fundamental tensors and submanifolds of a sphere

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Isometric Immersions which Preserve Curvature Operators

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Umbilics of constant curvature immersions

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Isometric immersions of constant curvature manifolds

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Global properties of minimal surfaces in \(E^ 3\) and \(E^ n\)

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Surfaces in the $4$-dimensional Euclidean space isometric to a sphere

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On parallel hypersurfaces of an elliptic hypersurface of the second order in \(E^{n+1}\)

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A theory of Riemannian submanifolds

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Pseudo-umbilical submanifolds with $M$-index $łeq 1$ in Euclidean spaces

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A note on pseudo-umbilical submanifolds with $M$-index $1$ and codimension $2$ in Euclidean spaces

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Submanifolds with a regular principal normal vector field in a sphere

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Minimal Hypersurfaces in a Riemannian Manifold of Constant Curvature

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Minimal submanifolds with M-index 2 in Riemannian manifolds of constant curvature

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Minimal submanifolds with M-index 2

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Minimal submanifolds with m-index 2 and generalized Veronese surfaces

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A theory of ruled surfaces in $E^{4}$

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Su certi sistemi \(\infty^ 2\) di rette associati ai punti di una superficie differenziabile di un iperspazio

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Über einen Satz von G. Ricci-Curbastro und die Gaußschen Krümmung der Minimalflächen. II

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Stationäre Krümmungsdichten auf Hperflächen des euklidischen \(R_{n+1}\)

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Applications of Stereographic Projections to Submanifolds in E m and S m

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Variational properties of functions of the mean curvatures for hypersurfaces in space forms

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Sur les variétés minimales \(V^ 2\) de E. Cartan dans un elliptique à \(n\) dimensions

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Sur les hypersurfaces minimales dans un espace elliptique à quatre et à cinq dimensions

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The Tension Field of the Gauss Map

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Local imbedding of Einstein spaces

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Hypersurfaces with parallel Ricci tensor

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Kähler manifolds as real hypersurfaces

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Submanifolds satisfying the condition $K(X,\,Y)\cdot K=0$

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Zur affinen Differentialgeometrie im Großen. I

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Closed Convex Hypersurfaces with Second Fundamental Form of Constant Curvature

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On some hypersurfaces satisfying R(X,Y)\(\cdot R_1\) = 0

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Some Integral Formulas for Closed Hypersurfaces in Euclidean Space

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Surfaces of curvatures $łambda =\mu =0$ in $E^{4}$

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Cylinders in Euclidean space $E^{2+n}$

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Zur Relativgeometrie: Symmetrische Zusammenhänge auf Hyperflächen

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Probleme der lokalen und globalen mehrdimensionalen Differentialgeometrie

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Charakterisierungen von Relativsphären und Ellipsoiden

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Anwendungen der De Rhamschen Zerlegung auf Probleme der lokalen Flächentheorie

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A note on minimal varieties

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Minimal varieties in Riemannian manifolds

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Submanifolds of constant mean curvature

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Gauss map in a sphere

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Homogeneous hypersurfaces in a sphere with the type number 2

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Minimal immersions of Riemannian manifolds

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Homogeneous hypersurfaces in spaces of constant curvature

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An isometric immersion of a homogeneous Riemannian manifold of dimension 3 in the hyperbolic space

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Rigidity for elliptic isometric imbeddings

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On hypersurfaces with constant $k$-th mean curvature

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Hypersurfaces satisfying a certain condition on the Ricci tensor

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Some hypersurfaces of a sphere

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Surfaces with vanishing normal curvature

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Pontrjagin classes of Riemannian manifolds of class 2

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Hypersurfaces of a Euclidean space $R^{4m}$

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On a part of a hypersurface, where the asymptotic tensor is of normal hyperbolic type

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The curvature groups of a hypersurface in the Euclidean space

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Submanifolds of Euclidean Space with Parallel Second Fundamental Form

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Sur une transformation hyperspatiale du problème des surfaces à coubures totale et moyenne linéairement liees, et sur quelques questions connexes

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Surfaces minimales du type de Riemann de E\(^4\) et groupes de transformations

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Variétés différentiables sans torsion.

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Über isotrope Strahlensysteme des pseudoeuklidischen Raumes <sup>1</sup><i>E</i><sup><i>n</i></sup>

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Untermannigfaltigkeiten mit paralleler zweiter Fundamentalform in Euklidischen Räumen und Sphären

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Extension of locally defined minimal immersions into spheres

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Über zweidimensionale parabolische Flächen im vierdimensional affinen Raum. I.

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Über Grenzübergänge in der Differentialgeometrie

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Zur projektiven Kinematik konjugierter Systeme des \(n\)-dimensionalen Raumes

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Eine Charakterisierung von Produkten geschlossener sphärischer Kurven

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Codazzi-Tensoren und Kennzeichnungen sphärischer Immersionen

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The Gauss Map in Spaces of Constant Curvature

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Positively curved n-manifolds in \(R^{n+2}\)

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Tight Immersions and Total Absolute Curvature†

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AN EXTENSION OF A RESULT OF BANG-YEN CHEN

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Some Minimal Imbeddings of Homogeneous Spaces

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Similarity Transformations of Hypersurfaces

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Integral Formulas for Submanifolds and their Applications

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Submanifolds with parallel mean curvature vector of a Euclidean space or a sphere

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On \((f,g,u,v,\lambda )\)-structures induced on a hypersurface of an odddimensional sphere

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Differential geometry of \(S^n \times S^n\)

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On the concurrent vector fields of immersed manifolds

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Submanifolds with parallel mean curvature vector

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Pseudo-umbilical submanifolds of codimension $2$

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Notes on hypersurfaces of an odd-dimensional sphere

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Submanifolds of codimension $2$ in an even-dimensional Euclidean space

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On normal $(f,\,g,\,u,\,v,\, \lambda)$-structures on submanifolds of codimension $2$ in an even-dimensional Euclidean space

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Integral formulas for closed hypersurfaces

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Torsion von Minimalflächen

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Ipersuperficie ricorrenti di uno spazio euclideo

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Identifiers

zbMATH Open document ID

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10.1007/BF01084984

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Mathematics Subject Classification ID

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zbMATH DE Number

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Sitelinks

Mathematics(1 entry)

mardi Publication:1133178

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