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arXiv · 1507.02575

Rigidity of compact pseudo-Riemannian homogeneous spaces for solvable Lie groups

Oliver Baues·Wolfgang Globke
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Abstract

Let $M$ be a compact connected pseudo-Riemannian manifold on which a solvable connected Lie group $G$ of isometries acts transitively. We show that $G$ acts almost freely on $M$ and that the metric on $M$ is induced by a bi-invariant pseudo-Riemannian metric on $G$. Furthermore, we show that the identity component of the isometry group of $M$ coincides with $G$.

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Oliver Baues, Wolfgang Globke. 2015-07-09. Rigidity of compact pseudo-Riemannian homogeneous spaces for solvable Lie groups. https://doi.org/10.1093/imrn%2Frnw320

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