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arXiv · 2006.04195

On locally homogeneous pseudo-Riemannian compact einstein manifolds

Maciej Bochenski·Aleksy Tralle
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Abstract

We ask a general question: what are locally homogeneous compact pseudo-Riemannian Einstein manifolds? We show that any standard compact Clifford-Klein form of a simple non-compact Lie group admits at least one Einstein metric. We conjecture that these are basically the only possible locally homogeneous Einstein pseudo-Riemannian compact manifolds using T. Kobayashi's conjecture as a guiding principle.

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Maciej Bochenski, Aleksy Tralle. 2020-06-07. On locally homogeneous pseudo-Riemannian compact einstein manifolds. https://doi.org/10.1016/j.geomphys.2020.103778

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