Abstract
We prove some rigidity results for compact manifolds with boundary. For a compact Riemannian manifold with nonnegative Ricci curvature and simply connected mean convex boundary, we show that if the sectional curvature vanishes on the boundary, the metric must be flat.
Original language | English (US) |
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Pages (from-to) | 283-287 |
Number of pages | 5 |
Journal | Pacific Journal of Mathematics |
Volume | 232 |
Issue number | 2 |
DOIs | |
State | Published - Oct 2007 |
Keywords
- Mean convex boundary
- Nonnegative Ricci curvature
- Reilly's formula
- Rigidity
ASJC Scopus subject areas
- General Mathematics