In this paper, we study $G$-g.o. metrics on compact homogeneous spaces $G/H$ with an intermediate subgroup $K$ such that $H\subset K\subset G$. In the beginning, we prove that the restricted metrics of $g$ on $K/H$ and $G/K$ are both g.o. metrics under certain conditions when $g$ is a $G$-g.o. metric on $G/H$. Then we develop several methods to determine $G$-g.o. metrics on $G/H$ by the representations of $K/H$ and $G/K$. As an application, we study g.o. metrics on a class of homogeneous spaces and find that $\mathrm{SO}(11)/(\mathrm{Spin}(7)\times \mathrm{SO}(2))$ admits non-naturally reductive g.o. metrics.
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Keywords: geodesic orbit manifold, representation of a compact Lie group, principal isotropy subgroup
Chen, Huibin 1 ; Chen, Zhiqi 2 ; Zhu, Fuhai 3
Chen, Huibin; Chen, Zhiqi; Zhu, Fuhai. Invariant geodesic orbit metrics on homogeneous spaces with intermediate subgroups. Journal of Lie Theory, Special issue dedicated to the memory of Joseph A. Wolf, Volume 36 (2026) no. 1, pp. 9-21. doi: 10.5802/jolt.1415
@article{10_5802_jolt_1415,
author = {Chen, Huibin and Chen, Zhiqi and Zhu, Fuhai},
title = {Invariant geodesic orbit metrics on homogeneous spaces with intermediate subgroups},
journal = {Journal of Lie Theory},
pages = {9--21},
year = {2026},
publisher = {XXXX},
volume = {36},
number = {1},
doi = {10.5802/jolt.1415},
language = {en},
url = {https://jolt.centre-mersenne.org/articles/10.5802/jolt.1415/}
}
TY - JOUR AU - Chen, Huibin AU - Chen, Zhiqi AU - Zhu, Fuhai TI - Invariant geodesic orbit metrics on homogeneous spaces with intermediate subgroups JO - Journal of Lie Theory PY - 2026 SP - 9 EP - 21 VL - 36 IS - 1 PB - XXXX UR - https://jolt.centre-mersenne.org/articles/10.5802/jolt.1415/ DO - 10.5802/jolt.1415 LA - en ID - 10_5802_jolt_1415 ER -
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