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Riemannian symmetries in flag manifolds

Paola PiuElisabeth Remm — 2012

Archivum Mathematicum

Flag manifolds are in general not symmetric spaces. But they are provided with a structure of 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 2 2 -symmetric structure to be naturally reductive are detailed for the flag manifold S O ( 5 ) / S O ( 2 ) × S O ( 2 ) × S O ( 1 ) .

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