Affiliation:
1. College of Mathematics and Systems Science , Shandong University of Science and Technology , Qingdao 266590 , P. R. China
2. Institute of Mathematics , School of Mathematical Sciences , 12534 Nanjing Normal University , Nanjing 210023 , P. R. China
Abstract
Abstract
In this article, we study the geodesic orbit Randers spaces of the form
(
G
/
H
,
F
)
{(G/H,F)}
, such that G is one of the compact classical Lie groups
SO
(
n
)
{{\mathrm{S}}{\mathrm{O}}(n)}
,
SU
(
n
)
{{\mathrm{S}}{\mathrm{U}}(n)}
,
Sp
(
n
)
{{\mathrm{S}}{\mathrm{p}}(n)}
, and H is a diagonally embedded product
H
1
×
⋯
×
H
s
{H_{1}\times\cdots\times H_{s}}
, where
H
i
{H_{i}}
is of the same type as G. Such spaces include spheres, Stiefel manifolds, Grassmann manifolds, and flag manifolds. The present work is a contribution to the study of geodesic orbit Randers spaces
(
G
/
H
,
F
)
{(G/H,F)}
with H semisimple. We construct new examples of non-Riemannian Randers g.o. metrics in homogeneous bundles over generalized Stiefel manifolds which are not naturally reductive. Also, we obtain the specific expressions of these Randers g.o. metrics.
Funder
National Natural Science Foundation of China
Natural Science Foundation of Shandong Province
Science and Technology Support Plan for Youth Innovation of Colleges and Universities of Shandong Province of China
Natural Science Research of Jiangsu Higher Education Institutions of China
Starting research funds of Shandong University of Science and Technology
Starting research funds of Nanjing Normal University