The Conjugate Loci and Cut Loci on Simply-Connected Lorentzian Symmetric Spaces

S. Deng ; X. Liu

Journal of Lie theory, Tome 24 (2014) no. 3, pp. 641-655.

Résumé

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.

Détail

Classification : 22E46, 53C30
Mots-clés : Lorentzian symmetric spaces, conjugate loci, cut loci, de Sitter spaces, Cahen-Wallach manifolds