Cohomogeneity-1 $AdS$ and Cohomogeneity-1 Myers-Perry Black Holes in $AdS$

Question

First that I am not a physicist, so sorry if my question is somehow vague!
I want to know if it is of any interest for physicists knowing about cohomogeneity-1 (C1) structures on Anti-de-sitter space ($AdS$) i.e., considering $AdS$ as a C1 manifold. If it is, could you briefly explain it or mention some usages.
As I read in some papers, Myers-Perry black holes in $AdS$, under some conditions (like being odd dimensional and having equal angular momenta) are C1. Is this fact related to C1 structures on $AdS$?

This post imported from StackExchange Physics at 2014-05-24 19:06 (UCT), posted by SE-user pmath