Low Dimensional Polar Actions

Abstract

Polar manifolds are Riemannian G-manifolds admitting a "section", i.e., a complete submanifold passing through every orbit and doing so orthogonally. We consider compact simply-connected polar manifolds and achieve an equivariantly diffeomorphic classification in dimensions 5 or less. As an application, we determine which of these polar actions admit an invariant metric with non-negative curvature.

Accepted for publication in Geometria Dedicata. Minor corrections from original version, 37 pages, 8 figures

References in corpus (2)

• Nonnegatively and Positively curved manifolds
• Nonnegatively curved 5-manifolds with non-abelian symmetry