Isometry groups of Lorentzian manifolds of finite volume and The local geometry of compact homogeneous Lorentz spaces

Details Isometry groups of Lorentzian manifolds of finite volume and The local geometry of compact homogeneous Lorentz spaces Isometry groups of Lorentzian manifolds of finite volume and The local geometry of compact homogeneous Lorentz spaces

2011-06-27

arxiv.org/abs/1106.5539v2

Mathematics

Differential Geometry

130 pages

Scientific paper

Based on the work of Adams and Stuck as well as on the work of Zeghib, we classify the Lie groups which can act isometrically and locally effectively on Lorentzian manifolds of finite volume. 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, we also describe the geometric structure of the manifolds if they are compact. 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, curvatures and holonomy. Especially, we obtain that any Ricci-flat compact homogeneous Lorentz space is flat or has compact isometry group.

Affiliated with

Also associated with

No associations

Rating

Isometry groups of Lorentzian manifolds of finite volume and The local geometry of compact homogeneous Lorentz spaces does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Isometry groups of Lorentzian manifolds of finite volume and The local geometry of compact homogeneous Lorentz spaces, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Isometry groups of Lorentzian manifolds of finite volume and The local geometry of compact homogeneous Lorentz spaces will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-40608