A Rigidity Theorem for the Hemisphere
Abstract
Description
We prove the following rigidity theorem: For an n-dimensional compact Riemannian manifold with boundary whose Ricci curvature is bounded by n-1 from below, if its boundary is isometric to the standard sphere of dimension n-1 and totally geodesic, then the manifold is isometric to the standard hemisphere.
The extrinsic boundary condition is relaxed
The extrinsic boundary condition is relaxed