Geodesic
Riemannian symmetries in flag manifolds
Archivum mathematicum, Tome 48 (2012) no. 5, pp. 387-398 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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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 $SO(5)/SO(2)\times SO(2) \times SO(1)$.
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 $SO(5)/SO(2)\times SO(2) \times SO(1)$.
DOI : 10.5817/AM2012-5-387
Classification : 53C30
Keywords: $\mathbb{Z}_2^k$-symmetric space; flag manifolds; Riemannian metrics 
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     author = {Piu, Paola and Remm, Elisabeth},
     title = {Riemannian symmetries in flag manifolds},
     journal = {Archivum mathematicum},
     pages = {387--398},
     year = {2012},
     volume = {48},
     number = {5},
     doi = {10.5817/AM2012-5-387},
     mrnumber = {3007620},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.5817/AM2012-5-387/}
}
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Piu, Paola; Remm, Elisabeth. Riemannian symmetries in flag manifolds. Archivum mathematicum, Tome 48 (2012) no. 5, pp. 387-398. doi: 10.5817/AM2012-5-387

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