The local geometry of compact homogeneous Lorentz spaces
Abstract
In 1995, S. Adams and G. Stuck as well as A. Zeghib independently provided a classification of non-compact Lie groups which can act isometrically and locally effectively on compact Lorentzian manifolds. In the case that the corresponding Lie algebra contains a direct summand isomorphic to the two-dimensional special linear algebra or to a twisted Heisenberg algebra, Zeghib also described the geometric structure of the manifolds. Using these results, we investigate the local geometry of compact homogeneous Lorentz spaces whose isometry groups have non-compact connected components. It turns out that they all are reductive. We investigate the isotropy representation and curvatures. In particular, we obtain that any Ricci-flat compact homogeneous Lorentz space is flat or has compact isometry group.
Keywords
Cite
@article{arxiv.1502.02622,
title = {The local geometry of compact homogeneous Lorentz spaces},
author = {Felix Günther},
journal= {arXiv preprint arXiv:1502.02622},
year = {2017}
}
Comments
20 pages. arXiv admin note: substantial text overlap with arXiv:1106.5539