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.
2012
Z^k_2-symmetric space; flag manifolds,; Riemannian metrics.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11584/44549
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