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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Rigidity theorems for nonpositive Einstein metrics


Author: Zhong Min Shen
Journal: Proc. Amer. Math. Soc. 116 (1992), 1107-1114
MSC: Primary 53C25; Secondary 53C20
MathSciNet review: 1123666
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Abstract: In this paper we study the following problem: When must a complete Einstein metric $ g$ on an $ n$-manifold with $ \operatorname{Ric} = (n - 1)\lambda {\text{g,}}\lambda \leq 0$, be a metric of constant curvature $ \lambda ?$


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1992-1123666-5
PII: S 0002-9939(1992)1123666-5
Keywords: Einstein metrics, rigidity, Sobolev inequality, the first eigenvalue, diameter, volume
Article copyright: © Copyright 1992 American Mathematical Society