G-manifolds with positive Ricci curvature and many isolated singular   orbits
  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. 
David J. Wraith
math.DG