Lower bound for \(L^{n/2}\) curvature norm and its application

DOI10.1007/BF02921626zbMath0960.53022OpenAlexW1982528752MaRDI QIDQ1298379

Katsuhiro Shiohama, Hong-Wei Xu

Publication date: 10 May 2001

Published in: The Journal of Geometric Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02921626

zbMATH Keywords

Betti numberssphere theoremNash isometric embedding

Mathematics Subject Classification ID

Global Riemannian geometry, including pinching (53C20)

Related Items (8)

Topological obstructions for submanifolds in low codimension ⋮ Integral curvature and topological obstructions for submanifolds ⋮ An eigenvalue pinching theorem for compact hypersurfaces in a sphere ⋮ Almost-Einstein hypersurfaces in the Euclidean space ⋮ Geometric properties for Gaussian image of submanifolds in \(S^{n+p} (1)\) ⋮ Almost conformally flat hypersurfaces ⋮ An integral formula for Lipschitz-Killing curvature and the critical points of height functions ⋮ Homology vanishing theorems for pinched submanifolds

Cites Work

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• On the total curvature of immersed manifolds. II
• Curvature, diameter and Betti numbers
• Diffeomorphism finiteness for manifolds with Ricci curvature and \(L^{n/2}\)-norm of curvature bounded
• L\({}^{n/2}\)-curvature pinching
• RIGIDITY AND SPHERE THEOREMS FOR SUBMANIFOLDS

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