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 Z22-symmetric space. We describe all the non degenerated metrics and classify the Riemannian and Lorentzian ones.
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