TY - JOUR
ID - 4454
TI - Rank inequality in homogeneous Finsler geometry
JO - AUT Journal of Mathematics and Computing
JA - AJMC
LA - en
SN - 2783-2449
AU - Xu, Ming
AD - School of Mathematical Sciences, Capital Normal University, Beijing 100048, P.R. China
Y1 - 2021
PY - 2021
VL - 2
IS - 2
SP - 171
EP - 184
KW - closed geodesic
KW - compact coset space
KW - homogeneous Finsler metric
KW - positive curvature
DO - 10.22060/ajmc.2021.20210.1058
N2 - This is a survey on some recent progress in homogeneous Finsler geometry. Three topics are discussed, the classification of positively curved homogeneous Finsler spaces, the geometric and topological properties of homogeneous Finsler spaces satisfying $K\geq0$ and the (FP) condition, and the orbit number of prime closed geodesics in a compact homogeneous Finsler manifold. These topics share the same similarity that the same rank inequality, i.e., $\mathrm{rank}G\leq\mathrm{rank}H+1$ for $G/H$ with compact $G$ and $H$, plays an important role. In this survey, we discuss in each topic how the rank inequality is proved, explain its importance, and summarize some relevant results.
UR - https://ajmc.aut.ac.ir/article_4454.html
L1 - https://ajmc.aut.ac.ir/article_4454_7c0a80121aaf6969c50902c807a75add.pdf
ER -