Address:
Dipartimento di Matematica e Informatica, Università degli Studi di Cagliari, Via Ospedale 72, 09124 Cagliari, Italia
Laboratoire de Mathématiques et Applications, Université de Haute Alsace, Faculté des Sciences et Techniques, 4, rue des Frères Lumière, 68 093 Mulhouse cedex, France
E-mail:
piu@unica.it
Elisabeth.Remm@uha.fr
Abstract: 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. The conditions for a metric adapted to the $\mathbb{Z}_2^2$-symmetric structure to be naturally reductive are detailed for the flag manifold $SO(5)/SO(2)\times SO(2) \times SO(1)$.
AMSclassification: primary 53C30.
Keywords: \mathbb{Z}_2^k-symmetric space, flag manifolds, Riemannian metrics.
DOI: 10.5817/AM2012-5-387