Gap theorems for certain submanifolds of Euclidean spaces and hyperbolic space forms

zbMath0642.53058MaRDI QIDQ1101705

Kunio Sugahara, Atsushi Kasue

Publication date: 1987

Published in: Osaka Journal of Mathematics (Search for Journal in Brave)

zbMATH Keywords

second fundamental formscalar curvaturesectional curvaturetotally geodesicminimal submanifoldgap theoremshyperbolic space formsopen submanifolds

Mathematics Subject Classification ID

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

Related Items (10)

Asymptotically flat manifolds of nonnegative curvature ⋮ On the total curvature and extrinsic area growth of surfaces with tamed second fundamental form ⋮ Ricci flatness of asymptotically locally Euclidean metrics ⋮ Comparison theorems and hypersurfaces ⋮ Density and spectrum of minimal submanifolds in space forms ⋮ Volume growth, number of ends, and the topology of a complete submanifold ⋮ Asymptotically extrinsic tamed submanifolds ⋮ A gap theorem for minimal submanifolds in Euclidean space ⋮ Energy estimates and Liouville theorems for harmonic maps ⋮ A convergence theorem for Riemannian manifolds and some applications

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