Orbit Spaces Arising from Isometric Actions on Hyperbolic Spaces

Let be a differentiable action of a Lie group on a differentiable manifold and consider the orbit space with the quotient topology.  Dimension of is called the cohomogeneity of the action of  on . If is a differentiable manifold  of  cohomogeneity one under the action of  a compact and connected Lie group, then the orbit space is homeomorphic to one of the spaces , , or . In this paper we suppose that the hyperbolic space  is of cohomogeneity  two under the action of , a connected and closed subgroup of  Then we prove that its orbit space is homeomorphic to  or  Also we prove that either all orbits are diffeomorphic to  or there are nonnegative integers   such that some orbits are diffeomorphic to , and the other orbits are diffeomorphic to , where may be a sphere, a homogeneous hypersurface of sphere or a helix in some Euclidean space. ../files/site1/files/0Abstract6.pdf