
Journal of Lie Theory 24 (2014), No. 3, 641655 Copyright Heldermann Verlag 2014 The Conjugate Loci and Cut Loci on SimplyConnected Lorentzian Symmetric Spaces Shaoqiang Deng School of Mathematical Sciences, Nankai University, Tianjin 300071, P. R. China dengsq@nankai.edu.cn Xingda Liu School of Mathematical Sciences, Nankai University, Tianjin 300071, P. R. China xingdaliu0924@sina.com [Abstractpdf] We study conjugate loci and cut loci of Lorentzian symmetric spaces. We prove that if $M_1$ is a connected simply connected Lorentzian symmetric space of the form $\mathbb{R}\times M$, $D\times M$, and $C\times M$, where $M$ is a connected simply connected compact Riemannian symmetric space, $D$ is the universal covering of the de Sitter spacetime with dimension $\geq3$, and $C$ is a CahenWallach manifold, then for any given point $x\in M_1$, all future (past) nonspacelike cut loci and the locus of first future (past) nonspacelike conjugate loci coincide. Keywords: Lorentzian symmetric spaces, conjugate loci, cut loci, de Sitter spaces, CahenWallach manifolds. MSC: 22E46, 53C30 [ Fulltextpdf (332 KB)] for subscribers only. 