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On Riemannian non symmetric spaces and flag manifolds

Abelkader Bouyakoub·Michel Goze·Elisabeth Remm
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Abstract

In this work we study riemannian metrics on flag manifolds adapted to the symmetries of these homogeneous nonsymmetric spaces. We first introduce the notion of riemannian $Γ$-symmetric space when $Γ$ is a general abelian finite group, the symmetric case corresponding to $Γ=\Z_2$. We describe and study all the riemannian metrics on $SO(2n+1)/SO(r_1)\times SO(r_2)\times SO(r_3)\times SO(2n+1-r_1-r_2-r_3)$ for which the symmetries are isometries. We consider also the lorentzian case and give an example of a lorentzian homogeneous space which is not a symmetric space.

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Abelkader Bouyakoub, Michel Goze, Elisabeth Remm. 2006-09-28. On Riemannian non symmetric spaces and flag manifolds. https://arxiv.org/abs/math/0609790

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