Metrics with homogeneous geodesics on flag manifolds

@article{Alekseevsky2002,
abstract = {A geodesic of a homogeneous Riemannian manifold $(M=G/K, g)$ is called homogeneous if it is an orbit of an one-parameter subgroup of $G$. In the case when $M=G/H$ is a naturally reductive space, that is the $G$-invariant metric $g$ is defined by some non degenerate biinvariant symmetric bilinear form $B$, all geodesics of $M$ are homogeneous. We consider the case when $M=G/K$ is a flag manifold, i.eȧn adjoint orbit of a compact semisimple Lie group $G$, and we give a simple necessary condition that $M$ admits a non-naturally reductive invariant metric with homogeneous geodesics. Using this, we enumerate flag manifolds of a classical Lie group $G$ which may admit a non-naturally reductive $G$-invariant metric with homogeneous geodesics.},
author = {Alekseevsky, Dimitri V., Arvanitoyeorgos, Andreas},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {homogeneous Riemannian spaces; homogeneous geodesics; flag manifolds; homogeneous Riemannian spaces; homogeneous geodesics; flag manifolds},
language = {eng},
number = {2},
pages = {189-199},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Metrics with homogeneous geodesics on flag manifolds},
url = {http://eudml.org/doc/248966},
volume = {43},
year = {2002},
}

TY - JOUR
AU - Alekseevsky, Dimitri V.
AU - Arvanitoyeorgos, Andreas
TI - Metrics with homogeneous geodesics on flag manifolds
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2002
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 43
IS - 2
SP - 189
EP - 199
AB - A geodesic of a homogeneous Riemannian manifold $(M=G/K, g)$ is called homogeneous if it is an orbit of an one-parameter subgroup of $G$. In the case when $M=G/H$ is a naturally reductive space, that is the $G$-invariant metric $g$ is defined by some non degenerate biinvariant symmetric bilinear form $B$, all geodesics of $M$ are homogeneous. We consider the case when $M=G/K$ is a flag manifold, i.eȧn adjoint orbit of a compact semisimple Lie group $G$, and we give a simple necessary condition that $M$ admits a non-naturally reductive invariant metric with homogeneous geodesics. Using this, we enumerate flag manifolds of a classical Lie group $G$ which may admit a non-naturally reductive $G$-invariant metric with homogeneous geodesics.
LA - eng
KW - homogeneous Riemannian spaces; homogeneous geodesics; flag manifolds; homogeneous Riemannian spaces; homogeneous geodesics; flag manifolds
UR - http://eudml.org/doc/248966
ER -