Journal of Lie Theory

no. 3
The Conjugate Loci and Cut Loci on Simply-Connected Lorentzian Symmetric Spaces
Journal of Lie Theory, Volume 24 (2014) no. 3, pp. 641-655
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.
DOI: 10.5802/jolt.799
Classification: 22E46, 53C30
Keywords: Lorentzian symmetric spaces, conjugate loci, cut loci, de Sitter spaces, Cahen-Wallach manifolds 
@article{JOLT_2014_24_3_a1,
     author = {S. Deng and X. Liu},
     title = {The {Conjugate} {Loci} and {Cut} {Loci} on {Simply-Connected} {Lorentzian} {Symmetric} {Spaces}},
     journal = {Journal of Lie Theory},
     pages = {641--655},
     year = {2014},
     volume = {24},
     number = {3},
     doi = {10.5802/jolt.799},
     zbl = {1307.53056},
     url = {https://jolt.centre-mersenne.org/articles/10.5802/jolt.799/}
}
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S. Deng; X. Liu. The Conjugate Loci and Cut Loci on Simply-Connected Lorentzian Symmetric Spaces. Journal of Lie Theory, Volume 24 (2014) no. 3, pp. 641-655. doi: 10.5802/jolt.799

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