On the Sectional Curvature of Compact Hypersurfaces

DOI10.2307/2048381zbMath0703.53046OpenAlexW4237383664MaRDI QIDQ3482495

Yoe Itokawa, Leslie Coghlan

Publication date: 1990

Full work available at URL: https://doi.org/10.2307/2048381

zbMATH Keywords

rigidity phenomenacompact immersed hypersurfacenormal ball

Mathematics Subject Classification ID

Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) (53C42) Global submanifolds (53C40)

Related Items (5)

On the Ricci curvature of a compact hypersurface in Euclidean space ⋮ On nonimmersibility of compact hypersurfaces into a ball of a simply connected space form ⋮ An integral formula for compact hypersurfaces in a Euclidean space and its applications ⋮ On the solutions to certain Laplace inequalities with applications to geometry of submanifolds ⋮ Rigidity of spheres in Riemannian manifolds and a non-embedding theorem

Cites Work

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• Isometric embedding of a compact Riemannian manifold into sphere
• An inequality between the exterior diameter and the mean curvature of bounded immersions
• A sufficient condition for a compact immersion to be spherical
• Elementary geometric applications of a maximum principle for nonlinear elliptic operators
• Isometric Immersions of Complete Riemannian Manifolds into Euclidean Space
• An Estimate for the Curvature of Bounded Submanifolds
• Isometric Embedding of a Compact Riemannian Manifold into Euclidean Space
• Some theorems on the isometric imbedding of compact Riemann manifolds in Euclidean space

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