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Vanishing sectional
curvature on the boundary and a conjecture of Schroeder and
Strake
Fengbo Hang and Xiaodong Wang |
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Vol. 232 (2007), No. 2, 283–287
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Abstract |
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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. |
Keywords
rigidity, nonnegative Ricci curvature, mean convex
boundary, Reilly’s formula
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Mathematical Subject Classification 2000
Primary: 53C24
Secondary: 53C21
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Milestones
Received: 4 September 2006
Revised: 2 February 2007
Accepted: 20 February 2007
Published: 1 October 2007
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Authors |
| Fengbo Hang | |
| Department of Mathematics Princeton University Fine Hall, Washington Road Princeton, NJ 08544 United States |
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| http://www.math.princeton.edu/~fhang | |
| Xiaodong Wang | |
| Department of Mathematics Michigan State University East Lansing, MI 48824 United States |
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| http://www.math.msu.edu/~xwang/ | |
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