A Rigidity Theorem for the Hemisphere
Differential Geometry
2007-12-03 v2
Abstract
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.
Cite
@article{arxiv.0711.4595,
title = {A Rigidity Theorem for the Hemisphere},
author = {Fengbo Hang and Xiaodong Wang},
journal= {arXiv preprint arXiv:0711.4595},
year = {2007}
}
Comments
The extrinsic boundary condition is relaxed