2017/07/04 by Zhiqi Chen, Joseph A. Wolf, Chen, Zhiqi +1
Mathematics · #22E10 #22E15 #53C30 #53C35 #53C50 #Advanced Algebra and Geometry #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Group Theory (math.GR)
paper · pdf · doi:10.48550/arxiv.1707.01181
openalex publication_date 2017/07/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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).