Rigidity theorems for nonpositive Einstein metrics

Shen, Zhong Min

doi:10.1090/S0002-9939-1992-1123666-5

Rigidity theorems for nonpositive Einstein metrics
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by Zhong Min Shen

Proc. Amer. Math. Soc. 116 (1992), 1107-1114

DOI: https://doi.org/10.1090/S0002-9939-1992-1123666-5

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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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