Homogeneous Lorentz manifolds with simple isometry group

Dave Witte

Homogeneous Lorentz manifolds with simple isometry group

Differential Geometry 2007-05-23 v1 Representation Theory

Authors: Dave Witte

Abstract

Let H be a closed, noncompact subgroup of a simple Lie group G, such that G/H admits an invariant Lorentz metric. We show that if G = SO(2,n), with n > 2, then the identity component of H is conjugate to the identity component of SO(1,n). Also, if G = SO(1,n), with n > 2, then the identity component of H is conjugate to the identity component of SO(1,n-1).

Keywords

lie groups holonomy homotopy groups

Cite

@article{arxiv.math/0007143,
  title  = {Homogeneous Lorentz manifolds with simple isometry group},
  author = {Dave Witte},
  journal= {arXiv preprint arXiv:math/0007143},
  year   = {2007}
}

Comments

Latex2e file, 9 pages, no figures

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