Rigidity and sphere theorem for manifolds with positive Ricci curvature

DOI10.1007/BF02568185zbMath0821.53034OpenAlexW2036623927MaRDI QIDQ1344557

Chang-Yu Xia

Publication date: 12 September 1995

Published in: Manuscripta Mathematica (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/156009

zbMATH Keywords

Ricci curvaturesphere theoremclosed immersed minimal submanifold

Mathematics Subject Classification ID

Geodesics in global differential geometry (53C22) Global Riemannian geometry, including pinching (53C20)

Related Items (11)

A sphere theorem for submanifolds in a manifold with pinched positive curvature ⋮ Diameter estimate of the manifolds with positive Ricci curvature and reverse volume pinching ⋮ Compact manifolds with positive \(m\)-Bakry-Émery Ricci tensor ⋮ Rigidity of compact manifolds with boundary and nonnegative Ricci curvature ⋮ A generalization of the classical sphere theorem ⋮ A rigidity phenomenon on Riemannian manifolds with reverse volume pinching ⋮ A gap phenomenon on Riemannian manifolds with reverse volume pinching ⋮ A differentiable sphere theorem on manifolds with reverse volume pinching ⋮ Smooth diameter and eigenvalue rigidity in positive Ricci curvature ⋮ A differentiable sphere theorem with positive Ricci curvature and reverse volume pinching ⋮ A rigidity phenomenon on Riemannian manifolds with reverse excess pinching

Cites Work

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• Manifolds near the boundary of existence
• The space of minimal embeddings of a surface into a three-dimensional manifold of positive Ricci curvature
• Oscillation criteria for self-adjoint second-order differential systems and Principal sectional curvatures
• Groups of polynomial growth and expanding maps. Appendix by Jacques Tits
• Eigenvalue comparison theorems and its geometric applications
• On the fundamental group of a compact minimal submanifolds
• A proof of the generalized Schoenflies theorem
• A Sphere Theorem for Reverse Volume Pinching on Even-Dimensional Manifolds
• Curvature of Closed Hypersurfaces and Non-Existence of Closed Minimal Hypersurfaces
• Riemannian geometry

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