Riemannian symmetries in flag manifolds

الأصل · EN

Flag manifolds are in general not symmetric spaces. But they are provided with a structure of Z₂ᵏ-symmetric space. We describe the Riemannian metrics adapted to this structure and some properties of reducibility. We detail for the flag manifold SO(5)/SO(2)× SO(2) × SO(1) what are the conditions for a metric adapted to the Z₂²-symmetric structure to be naturally reductive.