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arXiv · 0806.3169

Complete Einstein metrics are geodesically rigid

Volodymyr Kiosak·Vladimir S. Matveev
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Abstract

We prove that every complete Einstein (Riemannian or pseudo-Riemannian) metric $g$ is geodesically rigid: if any other complete metric $\bar g$ has the same (unparametrized) geodesics with $g$, then the Levi-Civita connections of $g$ and $\bar g$ coincide.

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Volodymyr Kiosak, Vladimir S. Matveev. 2008-07-09. Complete Einstein metrics are geodesically rigid. https://doi.org/10.1007/s00220-008-0719-7

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