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Semisimple weakly symmetric pseudo-Riemannian manifolds

  • Zhiqi Chen
  • Joseph A. Wolf
Article
  • 30 Downloads

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-Lorentzian signature \((n-2,2)\).

Keywords

Pseudo-Riemannian manifold Weakly symmetric space Real form family Lorentz manifold Trans-Lorentz manifold 

Mathematics Subject Classification

Primary 53C30 53C35 22E15 Secondary 53C50 22E46 

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Copyright information

© The Author(s) 2018

Authors and Affiliations

  1. 1.School of Mathematical Sciences and LPMCNankai UniversityTianjinPeople’s Republic of China
  2. 2.Department of MathematicsUniversity of CaliforniaBerkeleyUSA

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