Submanifolds with flat normal bundle

DOI10.1007/BF01457280zbMath0596.53049OpenAlexW2022055730MaRDI QIDQ5903193

Chun-Lian Terng

Publication date: 1987

Published in: Mathematische Annalen (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/164237

zbMATH Keywords

principal curvaturesDupin hypersurfacesisoparametric submanifoldstautnessweakly isoparametricWeingarten submanifold

Mathematics Subject Classification ID

Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) (53C42)

Related Items (20)

Infinitesimally homogeneous submanifolds of Euclidean spaces ⋮ Dupin hypersurfaces and integrable Hamiltonian systems of hydrodynamic type which do not possess Riemann invariants ⋮ Isometric immersions with prefixed second order geometry in minimal codimension ⋮ Wintgen ideal submanifolds: new examples, frame sequence and Möbius homogeneous classification ⋮ Submanifolds with flat normal bundle in spaces of constant curvature ⋮ Isoparametric hypersurfaces in spheres, integrable nondiagonalizable systems of hydrodynamic type, and \(N\)-wave systems ⋮ Contact properties of codimension 2 submanifolds with flat normal bundle ⋮ The Morse index of minimal products of minimal submanifolds in spheres ⋮ Singularities of parallels to tangent developable surfaces ⋮ A Berger type normal holonomy theorem for complex submanifolds ⋮ Immersions with totally reducible focal set ⋮ Surfaces with flat normal bundle: An explicit construction ⋮ On rigid string instantons in four dimensions ⋮ Bernstein type theorems with flat normal bundle ⋮ Isoparametric Submanifolds of Hyperbolic Spaces ⋮ On a class of submanifolds carrying an extrinsic totally umbilical foliation. ⋮ Conformally flat submanifolds in spheres and integrable systems ⋮ Normal and tangent maps to frontals ⋮ Isoparametric foliations on complex projective spaces ⋮ Classification of conformally flat isoparametric submanifolds of Euclidean space

Cites Work

• Dupin hypersurfaces
• Curvature properties of taut submanifolds
• Taut immersions of non-compact surfaces into a Euclidean 3-space
• Focal sets of submanifolds
• Isoparametric submanifolds and their Coxeter groups
• The fundamental equations of a submersion
• Minimal total absolute curvature for immersions
• Complete minimal surfaces in \(S^ 3\)
• On the Total Curvature of Immersed Manifolds
• Dupin Hypersurfaces
• Minimal hypersurfaces of S4 with non zero Gauss-Kronecker curvature
• Geometry and topology of isoparametric submanifolds in euclidean spaces
• Isoparametric Systems and Transnormality
• Morse Theory. (AM-51)
• Characteristic roots and vectors of a diifferentiable family of symmetric matrices^†
• Tight and Taut Immersions
• Umbilical Submanifolds and Morse Functions
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