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

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

2007-04-12

arxiv.org/abs/0704.1541v1

Mathematics

Differential Geometry

10 pages. In French

Scientific paper

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.

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