论文标题
在一类Abelian各向同性亚组的地球轨道空间上
On a class of geodesic orbit spaces with abelian isotropy subgroup
论文作者
论文摘要
Riemannian Geodesic轨道空间（g/h，g）是对称空间的自然概括，其特性由其大地测量的特性定义为G。我们研究形式（g/s，g）的一个参数亚组的轨道。我们给出了这些空间的简单几何表征，即它们是自然还原性的。反过来，这产生了在G/s形式的任何空间上不变的地球轨道（以及自然还原）指标的分类。我们的方法涉及通过将其研究减少到某些亚元号和广义的FLAG歧管，并研究与这些歧管相关的简单谎言代数的根系的性质，从而简化G/S上的复杂参数空间。
Riemannian geodesic orbit spaces (G/H,g) are natural generalizations of symmetric spaces, defined by the property that their geodesics are orbits of one-parameter subgroups of G. We study the geodesic orbit spaces of the form (G/S,g), where G is a compact, connected, semisimple Lie group and S is abelian. We give a simple geometric characterization of those spaces, namely that they are naturally reductive. In turn, this yields the classification of the invariant geodesic orbit (and also the naturally reductive) metrics on any space of the form G/S. Our approach involves simplifying the intricate parameter space of geodesic orbit metrics on G/S by reducing their study to certain submanifolds and generalized flag manifolds, and by studying properties of root systems of simple Lie algebras associated to these manifolds.
