On Riemannian nonsymmetric spaces and flag manifolds
نویسندگان
چکیده
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 = Z2. We describe and study all the riemannian metrics on SO(2n + 1)/SO(r1) × SO(r2) × SO(r3) × SO(2n + 1 − r1 − r2 − r3) 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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