Low Dimensional Polar Actions

2014/07/02 by Francisco J. Gozzi, Gozzi, Francisco J. · 2 citations
Mathematics · #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.1407.0638

openalex publication_date 2014/07/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Cited by

• On the Rational Hyperbolicity problem
• The dual foliation of polar actions on nonnegatively curved manifolds

Related

• Polar manifolds and actions
• Topics in polar actions
• Sections of polar actions
• Polar actions with a fixed point
• Extending tensors on polar manifolds