Semisimple Weakly Symmetric Pseudo--Riemannian Manifolds

Zhiqi Chen; Joseph A. Wolf

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arXiv · 1707.01181

Semisimple Weakly Symmetric Pseudo--Riemannian Manifolds

Zhiqi Chen·Joseph A. Wolf

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Abstract

We develop the classification of weakly symmetric pseudo--riemannian manifolds $G/H$ where $G$ is a semisimple Lie group and $H$ is a reductive subgroup. We derive the classification from the cases where $G$ is compact, and then we discuss the (isotropy) representation of $H$ on the tangent space of $G/H$ and the signature of the invariant pseudo--riemannian metric. As a consequence we obtain the classification of semisimple weakly symmetric manifolds of Lorentz signature $(n-1,1)$ and trans--Lorentz (conformal Lorentz) signature $(n-2,2)$.

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Zhiqi Chen, Joseph A. Wolf. 2017-07-04. Semisimple Weakly Symmetric Pseudo--Riemannian Manifolds. https://arxiv.org/abs/1707.01181

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