Flag manifolds are in general not symmetric spaces. But they are provided with a structure of Z^k_2-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 Z^2_2-symmetric structure to be naturally reductive.
RIEMANNIAN SYMMETRIES IN FLAG MANIFOLDS
PIU, MARIA PAOLA;
2012-01-01
Abstract
Flag manifolds are in general not symmetric spaces. But they are provided with a structure of Z^k_2-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 Z^2_2-symmetric structure to be naturally reductive.
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