Submanifolds and a Pinching Problem on the Second Fundamental Tensors

DOI10.2307/1996702zbMath0236.53043OpenAlexW4256700512MaRDI QIDQ5646072

Masafumi Okumura

Publication date: 1973

Full work available at URL: https://doi.org/10.2307/1996702

Mathematics Subject Classification ID

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

Related Items

Geometry and topology of submanifolds immersed in space forms and ellipsoids ⋮ Geometric, topological and differentiable rigidity of submanifolds in space forms ⋮ Differential geometry of submanifolds ⋮ The generalized Lu rigidity theorem for submanifolds with parallel mean curvature ⋮ Mean curvature flow of arbitrary codimension in complex projective spaces ⋮ Conformally Flat Spaces and a Pinching Problem on the Ricci Tensor ⋮ Generalized Ejiri's rigidity theorem for submanifolds in pinched manifolds ⋮ Kaehlerian manifolds with vanishing Bochner curvature tensor ⋮ A pinching problem on submanifolds with parallel mean curvature vector field in a sphere ⋮ Some characterizations of space-forms ⋮ Conformally Flat Manifolds and a Pinching Problem on the Ricci Tensor ⋮ A pinching problem on the second fundamental tensors and submanifolds of a sphere ⋮ Hypersurfaces in a sphere with constant mean curvature ⋮ A rigidity theorem for submanifolds with parallel mean curvature in a sphere

Cites Work

• A formula of Simons' type and hypersurfaces with constant mean curvature
• Submanifolds with parallel mean curvature vector
• Hypersurfaces and a Pinching Problem on the Second Fundamental Tensor
• Curvature and Betti Numbers. (AM-32)