Riemannian symmetries in flag manifolds

Details Riemannian symmetries in flag manifolds Riemannian symmetries in flag manifolds

2012-04-11

arxiv.org/abs/1204.2440v1

Mathematics

Differential Geometry

11 pages

Scientific paper

Flag manifolds are in general not symmetric spaces. But they are provided with a structure of $\mathbb{Z}_2^k$-symmetric space. We describe the Riemannian metrics adapted to this structure and some properties of reducibility. We detail for the flag manifold $SO(5)/SO(2)\times SO(2) \times SO(1)$ what are the conditions for a metric adapted to the $\mathbb{Z}_2^2$-symmetric structure to be naturally reductive.

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