Lie transformation groups in Riemannian geometry

我们计划研究的领域可以被描述为黎曼几何中的李变换群。重点将是紧李群在欧几里德空间和紧对称空间上的等距作用，但更一般的黎曼流形也将被考虑。我们的目标是理解黎曼流形上一些最有趣的动作的轨道的几何和拓扑结构。方法将是几何和代数。

The area in wich we plan to work can be described as Lie transformation groups in Riemannian Geometry. The emphasis will be on isometric actions of compact Lie groups on Euclidean spaces and compact symmetric spaces, but more general Riemannian manifolds will also be considered. The goal is to understand the geometry and topology of the orbits of some of the most interesting classes of actions on Riemannian manifolds. The methods will be both geometric and algebraic.