A general rigidity theorem for complete submanifolds

DOI10.1017/S0027763000025083zbMath0911.53035OpenAlexW1545158479MaRDI QIDQ4209783

Katsuhiro Shiohama, Hong-Wei Xu

Publication date: 28 April 1999

Published in: Nagoya Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1017/s0027763000025083

zbMATH Keywords

Riemannian manifoldrigiditypinchingsubmanifolds with parallel mean curvature vector

Mathematics Subject Classification ID

Global submanifolds (53C40)

Related Items (16)

Characterization of Whitney spheres among Lagrangian submanifolds with conformal Maslov form ⋮ On the principal curvatures of complete minimal hypersurfaces in space forms ⋮ Gap theorems for Lagrangian submanifolds in complex space forms ⋮ The generalized Lu rigidity theorem for submanifolds with parallel mean curvature ⋮ Mean curvature flow of arbitrary codimension in complex projective spaces ⋮ On rigidity of Clifford torus in a unit sphere ⋮ 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 ⋮ On complete submanifolds with parallel mean curvature in negative pinched manifolds ⋮ Generalized Ejiri's rigidity theorem for submanifolds in pinched manifolds ⋮ Closed hypersurfaces with constant mean curvature in a symmetric manifold ⋮ Geometric rigidity theorem for submanifolds with positive curvature ⋮ Rigidity of closed submanifolds in a locally symmetric Riemannian manifold ⋮ An optimal rigidity theorem for complete submanifolds in a sphere ⋮ Submanifolds with parallel Gaussian mean curvature vector in Euclidean spaces ⋮ Global rigidity theorems for submanifolds with parallel mean curvature

Cites Work

• An intrinsic rigidity theorem for minimal submanifolds in a sphere
• A rigidity theorem for submanifolds with parallel mean curvature in a sphere
• Isometric immersions of Riemannian manifolds
• Local rigidity theorems for minimal hypersurfaces
• Minimal varieties in Riemannian manifolds
• Rigidity theorems in rank-1 symmetric spaces
• Harmonic functions on complete riemannian manifolds
• Submanifolds with Constant Mean Curvature

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