Polar homogeneous foliations on hyperbolic spaces

Abstract: An isometric action of a Lie group on a Riemannian manifold is polar if it admits a section (that is, a submanifold that meets every orbit orthogonally). These actions generalize several well-known concepts in geometry, such as the polar coordinate system in the Euclidean plane or the spectral theorem for self-adjoint operators. Because of this, an active research topic has been the classification of polar actions on Riemannian manifolds with a relatively large group of isometries, such as symmetric spaces.

In this talk, I will discuss a joint work work with José Carlos Díaz-Ramos (Universidade de Santiago de Compostela) in which we classify polar actions without singular orbits (also known as polar homogeneous foliations) on quaternionic hyperbolic spaces and the Cayley hyperbolic plane. This result closes the classification problem for such actions on symmetric spaces of noncompact type and rank one.

differential geometry

Audience: researchers in the topic

( paper )

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Virtual seminar on geometry with symmetries

Series comments: Description: Research seminar in Lie group actions in Differential geometry.

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