Riemannian symmetries in flag manifolds
Copyright policy )Riemannian symmetries in flag manifolds
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.
11 pages
- University of Cagliari Italy
- University of Upper Alsace France
Mathematics - Differential Geometry, flag manifolds, Z^k_2-symmetric space; flag manifolds,; Riemannian metrics., Differential Geometry (math.DG), FOS: Mathematics, 53C30, [MATH.MATH-GM] Mathematics [math]/General Mathematics [math.GM], Riemannian metrics
Mathematics - Differential Geometry, flag manifolds, Z^k_2-symmetric space; flag manifolds,; Riemannian metrics., Differential Geometry (math.DG), FOS: Mathematics, 53C30, [MATH.MATH-GM] Mathematics [math]/General Mathematics [math.GM], Riemannian metrics
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