On Riemannian non symmetric spaces and flag manifolds

2006/09/28 by Bouyakoub, Abelkader, Goze, Michel, Remm, Elisabeth
#53C20 53C35 #Differential Geometry (math.DG) #FOS: Mathematics #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.math/0609790

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=\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.

Related

• Riemannian symmetries in flag manifolds
• Pseudo-Riemannian Symmetries on Heisenberg group ℍ₃
• Pseudo-Riemannian Symmetries on Heisenberg groups
• Riemannian and Lorentzian structures on the non symmetric space SO(2m)/Sp(m)
• On formality of generalized symmetric spaces