Cohomogeneity One Manifolds and Homogeneous Spaces of Positive Scalar Curvature

TL;DR

This paper characterizes cohomogeneity one manifolds and homogeneous spaces that admit invariant metrics with positive scalar curvature, providing a classification of such geometric structures under compact Lie group actions.

Contribution

It offers a complete characterization of cohomogeneity one manifolds and homogeneous spaces with positive scalar curvature under compact Lie group actions, advancing understanding in geometric analysis.

Findings

Classification of cohomogeneity one manifolds with positive scalar curvature

Characterization of homogeneous spaces with invariant positive scalar curvature

Identification of conditions for existence of such metrics

Abstract

We characterize cohomogeneity one manifolds and homogeneous spaces with a compact Lie group action admitting an invariant metric with positive scalar curvature.