Riemannian symmetries in flag manifolds

2012/04/11 by Piu, Paola, Remm, Elisabeth
#53C30 #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1204.2440

Abstract

Flag manifolds are in general not symmetric spaces. But they are provided with a structure of ℤ₂^k-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.

Related

• On Riemannian non symmetric spaces and flag manifolds
• Riemannian and Lorentzian structures on the non symmetric space SO(2m)/Sp(m)
• (Z/2Z x Z/2Z)-symmetric spaces
• The index of symmetry of compact naturally reductive spaces
• Flag Manifolds and Grassmannians