Riemannian symmetries in flag manifolds
Archivum Mathematicum (2012)
- Volume: 048, Issue: 5, page 387-398
- ISSN: 0044-8753
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topPiu, Paola, and Remm, Elisabeth. "Riemannian symmetries in flag manifolds." Archivum Mathematicum 048.5 (2012): 387-398. <http://eudml.org/doc/251409>.
@article{Piu2012,
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 $SO(5)/SO(2)\times SO(2) \times SO(1)$.},
author = {Piu, Paola, Remm, Elisabeth},
journal = {Archivum Mathematicum},
keywords = {$\mathbb \{Z\}_2^k$-symmetric space; flag manifolds; Riemannian metrics; -symmetric space; flag manifold; Riemannian metrics},
language = {eng},
number = {5},
pages = {387-398},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {Riemannian symmetries in flag manifolds},
url = {http://eudml.org/doc/251409},
volume = {048},
year = {2012},
}
TY - JOUR
AU - Piu, Paola
AU - Remm, Elisabeth
TI - Riemannian symmetries in flag manifolds
JO - Archivum Mathematicum
PY - 2012
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 048
IS - 5
SP - 387
EP - 398
AB - 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 $SO(5)/SO(2)\times SO(2) \times SO(1)$.
LA - eng
KW - $\mathbb {Z}_2^k$-symmetric space; flag manifolds; Riemannian metrics; -symmetric space; flag manifold; Riemannian metrics
UR - http://eudml.org/doc/251409
ER -
References
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