The geometry of surfaces in 4-space from a contact viewpoint
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Publication:1900023
DOI10.1007/BF01265348zbMath0834.53006OpenAlexW1996512479MaRDI QIDQ1900023
Publication date: 17 April 1996
Published in: Geometriae Dedicata (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/bf01265348
Surfaces in Euclidean and related spaces (53A05) Convex sets in (n) dimensions (including convex hypersurfaces) (52A20) Theory of singularities and catastrophe theory (58K99) Differentiable maps on manifolds (58C25)
Related Items (48)
Singularities of lightcone pedals of spacelike curves in Lorentz-Minkowski 3-space ⋮ Affine metrics of locally strictly convex surfaces in affine 4-space ⋮ Conformal invariants and spherical contacts of surfaces in \(\mathbb R^4\) ⋮ Gauss maps on canal hypersurfaces of generic curves in \(\mathbb{R}^4\) ⋮ The Wigner caustic on shell and singularities of odd functions ⋮ Contact properties of codimension 2 submanifolds with flat normal bundle ⋮ Singularities of caustics of surfaces in non-flat Riemannian 4-space form ⋮ A new approach to canal surface with parallel transport frame ⋮ The flat geometry of the I_1 singularity: (x,y) -> (x,xy,y^2,y^3) ⋮ Invariants and quasi-umbilicity of timelike surfaces in Minkowski space \(\mathbb R^{3,1}\) ⋮ ASYMPTOTIC CURVES ON SURFACES IN ℝ5 ⋮ The curvature Veronese of a 3-manifold immersed in Euclidean space ⋮ Critical points of the Gauss map and the exponential tangent map ⋮ Affine metric for locally strictly convex manifolds of codimension 2 ⋮ Lightlike hypersurfaces and canal hypersurfaces of Lorentzian surfaces ⋮ Inflection points and nonsingular embeddings of surfaces in \(\mathbb{R}^5\) ⋮ Semiumbilic points for minimal surfaces in Euclidean 4-space ⋮ Geometric invariants of surfaces in \(\mathbb R^4\). ⋮ Self-conjugate vectors of immersed 3-manifolds in \(\mathbb{R}^6\) ⋮ Geometry of curves and surfaces through the contact map ⋮ A note on binary quintic forms and lines of principal curvature on surfaces in \(\mathbb{R}^5\) ⋮ The geometry of corank 1 surfaces in ℝ4 ⋮ Relating second order geometry of manifolds through projections and normal sections ⋮ PROJECTIONS OF HYPERSURFACES IN ℝ4 WITH BOUNDARY TO PLANES ⋮ Geometry of surfaces in \(\mathbb{R}^5\) through projections and normal sections ⋮ The horospherical geometry of surfaces in hyperbolic 4-space ⋮ Inflection points and asymptotic lines on Lagrangian surfaces ⋮ Generic affine differential geometry of space curves ⋮ Singularities of Anti de Sitter torus Gauss maps ⋮ Singularities of affine equidistants: extrinsic geometry of surfaces in 4-space ⋮ Normal and tangent maps to frontals ⋮ Birth of bitangencies in a family of surfaces in \(\mathbb{R}^{4}\) ⋮ Inflection points and topology of surfaces in 4-space ⋮ Codazzi fields on surfaces immersed in Euclidean 4-space ⋮ Orthogonal asymptotic lines on surfaces immersed in \(\mathbb{R}^4\) ⋮ Generic geometry of stable maps of 3-manifolds into \(\mathbb{R}^4\) ⋮ Cross-ratio invariants for surfaces in 4-space ⋮ The Taylor expansion of the exponential map and geometric applications ⋮ Self-adjoint operators on surfaces in \(\mathbb R^n\) ⋮ The bi-normal fields on spacelike surfaces in ℝ14 ⋮ Geometric contacts of surfaces immersed in \(\mathbb R^n,n\geqslant 5\) ⋮ Singular 3-manifolds in \(\mathbb{R}^5\) ⋮ A relation between the curvature ellipse and the curvature parabola ⋮ Asymptotic and binormal directions on surfaces sitting in the four-dimensional Euclidean space ⋮ Asymptotic lines on real Milnor links of a family that realizes any genus ⋮ Contact properties of surfaces in \({\mathbb R}^3\) with corank 1 singularities ⋮ Semiumbilics and 2-regular immersions of surfaces in Euclidean spaces ⋮ Umbilicity of surfaces with orthogonal asymptotic lines in \(\mathbb R^ 4\).
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