Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry, Vol. 42, No. 2, pp. 451-461 (2001)
Homogeneous Lorentz Manifolds with Simple Isometry Group
Dave Witte
Department of Mathematics, Oklahoma State University, Stillwater, OK 74078, e-mail: dwitte@math.okstate.edu
Abstract: \def{\SO}{ SO} 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 $n \ge 3$, then the identity component $H^\circ$ of $H$ is conjugate to $\SO(1,n)^\circ$. Also, if $G = \SO(1,n)$, with $n \ge 3$, then $H^\circ$ is conjugate to $\SO(1,n-1)^\circ$.
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