Low Dimensional Polar Actions
Differential Geometry
2014-11-12 v2
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.
Cite
@article{arxiv.1407.0638,
title = {Low Dimensional Polar Actions},
author = {Francisco J. Gozzi},
journal= {arXiv preprint arXiv:1407.0638},
year = {2014}
}
Comments
Accepted for publication in Geometria Dedicata. Minor corrections from original version, 37 pages, 8 figures