Geodesic
Metrics with homogeneous geodesics on flag manifolds
Commentationes Mathematicae Universitatis Carolinae, Tome 43 (2002) no. 2, pp. 189-199.

Voir la notice de l'article provenant de la source Czech Digital Mathematics Library

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.e\. an 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.
Classification : 03E25, 14M15, 53C22, 53C30
Keywords: homogeneous Riemannian spaces; homogeneous geodesics; flag manifolds 
@article{CMUC_2002__43_2_a0,
     author = {Alekseevsky, Dmitri and Arvanitoyeorgos, Andreas},
     title = {Metrics with homogeneous geodesics on flag manifolds},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     pages = {189--199},
     publisher = {mathdoc},
     volume = {43},
     number = {2},
     year = {2002},
     mrnumber = {1922121},
     zbl = {1090.53044},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMUC_2002__43_2_a0/}
}
TY  - JOUR
AU  - Alekseevsky, Dmitri
AU  - Arvanitoyeorgos, Andreas
TI  - Metrics with homogeneous geodesics on flag manifolds
JO  - Commentationes Mathematicae Universitatis Carolinae
PY  - 2002
SP  - 189
EP  - 199
VL  - 43
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/CMUC_2002__43_2_a0/
LA  - en
ID  - CMUC_2002__43_2_a0
ER  - 
%0 Journal Article
%A Alekseevsky, Dmitri
%A Arvanitoyeorgos, Andreas
%T Metrics with homogeneous geodesics on flag manifolds
%J Commentationes Mathematicae Universitatis Carolinae
%D 2002
%P 189-199
%V 43
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/CMUC_2002__43_2_a0/
%G en
%F CMUC_2002__43_2_a0
Alekseevsky, Dmitri; Arvanitoyeorgos, Andreas. Metrics with homogeneous geodesics on flag manifolds. Commentationes Mathematicae Universitatis Carolinae, Tome 43 (2002) no. 2, pp. 189-199. http://geodesic.mathdoc.fr/item/CMUC_2002__43_2_a0/