地点：行健楼学术活动室526
摘要：This talk can be divided into three parts. In the first part, we will show some new examples of non-naturally reductive Einstein metrics on compact simple Lie groups by using the structure of generalized Wallach spaces. We will also show a better lower boundary of the number of non-naturally reductive Einstein metrics on SO(n) and Sp(n).
In the second part, we will show that all geodesic orbit metrics on compact simple arising from generalized Wallach spaces and flag manifolds are naturally reductive.
In the third part, we will show our recent results on geodesic orbit metrics. We will show that all geodesic orbit metrics on compact simple Lie groups arising from homogeneous spaces with 2 and 3 isotropy summands are naturally reductive. Furthermore, we obtain a theorem, which indicates that most of the geodesic orbit metrics on compact simple Lie groups are naturally reductive. Besides, we form some new geodesic orbit metrics on homogeneous spaces with semi-simple isometry groups.