Symmetric spaces and polar actions

Andreas Kollross - Universität Augsburg.

Resumo:

An isometric action of a Lie group on a Riemannian manifold is called polar if there is a submanifold whose intersections with the group orbits are everywhere orthogonal and which meets all orbits. Polar actions are a very special class of Lie group actions with many distinguished geometric properties and they are closely related to the theory of symmetric spaces in more than one way. In this short series of lectures, I will give a survey on polar actions and related topics, focusing on classification results. I will start with an introduction to symmetric spaces and I will recall some basics about semisimple Lie groups and their representation theory needed for the later two talks. Then I will turn to polar actions, discuss examples, fundamental results and relations to submanifold geometry. In the last part, I will talk about recent results.

© Andreas Kollross.