Riemannian and Lorentzian structures on the non symmetric space SO(2m)/Sp(m)

2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/127266In this work, we are interested in a non symmetric homogeneous space, namely $SO(2m)/Sp(m)$. We show that this space admits a structure of $Z_2^2$-symmetric space. We describe all the non degenerated metrics and classify the Riemannian and Lorentzian ones.10 pages. In FrenchDifferential GeometryRings and Algebras53C30; 53C20 ; 53C50 ; 17BxxRiemannian and Lorentzian structures on the non symmetric space SO(2m)/Sp(m)text