The differentiable sphere theorem for manifolds with positive Ricci curvature

DOI10.1090/S0002-9939-2011-10952-3zbMath1242.53063OpenAlexW2060436837MaRDI QIDQ2880662

Juan-Ru Gu, Hong-Wei Xu

Publication date: 13 April 2012

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0002-9939-2011-10952-3

zbMATH Keywords

Ricci flowdifferentiable sphere theorem\(k\)-th Ricci curvature

Mathematics Subject Classification ID

Global submanifolds (53C40) Global Riemannian geometry, including pinching (53C20)

Cites Work

• Classification of manifolds with weakly 1/4-pinched curvatures
• A general convergence result for the Ricci flow in higher dimensions
• Topological and differentiable sphere theorems for complete submanifolds
• Contracting convex hypersurfaces in Riemannian manifolds by their mean curvature
• Oscillation criteria for self-adjoint second-order differential systems and Principal sectional curvatures
• The Jacobi equation on naturally reductive compact Riemannian homogeneous spaces
• Three-manifolds with positive Ricci curvature
• An optimal differentiable sphere theorem for complete manifolds
• Manifolds with positive curvature operators are space forms
• Differenzierbare Strukturen und Metriken positiver Krümmung auf Sphären
• Manifolds with 1/4-pinched curvature are space forms
• Classification of almost quarter-pinched manifolds
• Sphere Theorems in Geometry
• On Complete Manifolds of Nonnegative kth-Ricci Curvature
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