G-manifolds with positive Ricci curvature and many isolated singular orbits

Abstract

We show that in cohomogeneity 3 there are G-manifolds with any given number of isolated singular orbits and an invariant metric of positive Ricci curvature. We show that the corresponding result is also true in cohomogeneity 5 provided the number of singular orbits is even.

arXiv comment19 pages. This paper has been substantially re-written to improve the exposition, to present the technical details in greater generality, and to correct a mistake in the second section of the original version. The main results are unchanged