A Rigidity Theorem for the Hemisphere

Details A Rigidity Theorem for the Hemisphere A Rigidity Theorem for the Hemisphere

2007-11-28

arxiv.org/abs/0711.4595v2

Mathematics

Differential Geometry

The extrinsic boundary condition is relaxed

Scientific paper

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.

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