Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Some rigidity phenomena for Einstein metrics

Author: Zhong Min Shen
Journal: Proc. Amer. Math. Soc. 108 (1990), 981-987
MSC: Primary 53C25; Secondary 53C20
MathSciNet review: 1007511
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Abstract: In this note we study the following problem: When must a complete Einstein metric $ g$ on an $ n$-manifold with $ {\text{Ric = }}(n - 1)\lambda g$ be a constant curvature metric of sectional curvature $ \lambda $?

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Keywords: Sobolev inequality, Einstein metric, volume, rigidity
Article copyright: © Copyright 1990 American Mathematical Society