Let M= G/ H be a compact, simply connected, Riemannian homogeneous space, where G is (almost) effective and H is a simple Lie group. In this paper, we first classify all G-naturally reductive metrics on M, and then all G-geodesic orbit metrics on M.
Funding
This work was supported by National Natural Science Foundation of China (11931009)
and Natural Science Foundation of Tianjin (19JCYBJC30600). The second author was partially supported by
the Australian Research Council Discovery Grant DP210100951.