On the curvature of G-manifolds with finitely many non-principal orbits
  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. 
Stefan Bechtluft-Sachs, David J. Wraith
math.DG