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

Oliver Baues; Wolfgang Globke

doi:10.1093/imrn/rnw320

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

Differential Geometry 2018-05-22 v1

Authors: 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 $G$ .

Keywords

pseudo-Riemannian homogeneous space solvable Lie group rigidity almost free action bi-invariant metric isometry group

Cite

@article{arxiv.1507.02575,
  title  = {Rigidity of compact pseudo-Riemannian homogeneous spaces for solvable Lie groups},
  author = {Oliver Baues and Wolfgang Globke},
  journal= {arXiv preprint arXiv:1507.02575},
  year   = {2018}
}

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