Global pinching theorems for even dimensional minimal submanifolds in the unit spheres

DOI10.1007/BF01214903zbMath0651.53044OpenAlexW2078865067MaRDI QIDQ1106492

Chang-Yu Xia, Jun-Min Lin

Publication date: 1989

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

Full work available at URL: https://eudml.org/doc/174060

zbMATH Keywords

totally geodesicminimal submanifoldsPontrjagin numberspinching theorem

Mathematics Subject Classification ID

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

Related Items (7)

Characterizations of complete spacelike submanifolds in the \((n+p)\)-dimensional anti-de Sitter space of index \(q\) ⋮ On energy gap phenomena of the Whitney spheres in \(\mathbb{C}^n\) or \(\mathbb{CP}^n\) ⋮ A gap theorem for complete submanifolds with parallel mean curvature in the hyperbolic space ⋮ \(L^2\)-isolation phenomenon for complete surfaces arising from Yang-Mills theory ⋮ Submanifolds with parallel Gaussian mean curvature vector in Euclidean spaces ⋮ A lower bound for 𝐿₂ length of second fundamental form on minimal hypersurfaces ⋮ Global rigidity theorems for submanifolds with parallel mean curvature

Cites Work

• Minimal varieties in Riemannian manifolds
• Heat Equations on Minimal Submanifolds and Their Applications
• Minimal Submanifolds of a Sphere with Second Fundamental Form of Constant Length
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