A Sphere Theorem for Submanifolds in a Manifold with Pinched Positive Curvature.
Global Pinching Theorems for Even Dimensional Minimal Submanifolds in the Unit Sphere.
Topological and metric rigidity teorems for hypersurfaces in a hyperbolic space
In this paper we study the topological and metric rigidity of hypersurfaces in , the -dimensional hyperbolic space of sectional curvature . We find conditions to ensure a complete connected oriented hypersurface in to be diffeomorphic to a Euclidean sphere. We also give sufficient conditions for a complete connected oriented closed hypersurface with constant norm of the second fundamental form to be totally umbilic.
Page 1