On the curvature of G-manifolds with finitely many non-principal orbits

TL;DR

This paper studies the curvature properties of G-manifolds with limited non-principal orbits, establishing existence results for metrics with positive Ricci and non-negative sectional curvature, and exploring applicable examples.

Contribution

It provides new existence theorems for invariant metrics with specific curvature conditions on G-manifolds with finitely many non-principal orbits.

Findings

Existence of metrics with positive Ricci curvature

Existence of metrics with non-negative sectional curvature

Application to specific families of G-manifolds

Abstract

We investigate the curvature of invariant metrics on G-manifolds with finitely many non-principal orbits. We prove existence results for metrics of positive Ricci curvature and non-negative sectional curvature, and discuss some families of examples to which these existence results apply.