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arXiv · 2409.15707

Rigidity for Einstein manifolds under bounded covering geometry

Cuifang Si·Shicheng Xu
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Abstract

In this note we prove three rigidity results for Einstein manifolds with bounded covering geometry. (1) An almost flat manifold $(M,g)$ must be flat if it is Einstein, i.e. $\operatorname{Ric}_g=\lambda g$ for some real number $\lambda$. (2) A compact Einstein manifolds with a non-vanishing and almost maximal volume entropy is hyperbolic. (3) A compact Einstein manifold admitting a uniform local rewinding almost maximal volume is isometric to a space form.

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Cuifang Si, Shicheng Xu. 2024-09-24. Rigidity for Einstein manifolds under bounded covering geometry. https://doi.org/10.4208/jms.v58n2.25.02

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