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

Abstract

In 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 French