Journal of Lie Theory 24 (2014), No. 3, 641--655
Copyright Heldermann Verlag 2014
The Conjugate Loci and Cut Loci on Simply-Connected 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
[Abstract-pdf]
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 space-time with dimension $\geq3$, and $C$ is a Cahen-Wallach 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, Cahen-Wallach manifolds.
MSC: 22E46, 53C30
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