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URL: http://mmr.khu.ac.ir/article-1-2596-en.html
2- imam KIhomeini International University
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
Received: 2017/01/30 | Revised: 2018/05/12 | Accepted: 2017/10/8 | Published: 2017/10/9 | ePublished: 2017/10/9
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