On homogeneous manifolds whose isotropy actions are polar

2018/05/09 by Diaz-Ramos, Jose Carlos, Dominguez-Vazquez, Miguel, Kollross, Andreas
#53C30 #53C35 #57S15 #57S20 #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1805.03619

Abstract

We show that simply connected Riemannian homogeneous spaces of compact semisimple Lie groups with polar isotropy actions are symmetric, generalizing results of Fabio Podesta and the third named author. Without assuming compactness, we give a classification of Riemannian homogeneous spaces of semisimple Lie groups whose linear isotropy representations are polar. We show for various such spaces that they do not have polar isotropy actions. Moreover, we prove that Heisenberg groups and non-symmetric Damek-Ricci spaces have non-polar isotropy actions.

Related

• Polar manifolds and actions
• Polar actions on Hermitian and quaternion-Kähler symmetric spaces
• Coisotropic and polar actions on compact irreducible Hermitian symmetric spaces
• Polar actions with a fixed point
• Polar actions on homogeneous 3-spaces