Horospherical flat surfaces in Hyperbolic 3space
Preprint Series # 838 Izumiya, Shyuichi and Saji, Kentaro and Takahashi, Masatomo Horospherical flat surfaces in Hyperbolic 3space. (2007); Abstract Recently we discovered a new geometry on submanifolds in
hyperbolic $n$space
which is called {\it horospherical geometry}.
Unfortunately this geometry is not invariant under
the hyperbolic motions (it is invariant under the canonical action of
$SO(n)$), but it has quite interesting
features.
For example, the flatness in this geometry is
a hyperbolic invariant and the total curvatures are topological invariants.
In this paper, we investigate the {\it horospherical flat surfaces}
(flat surfaces
in the sense of horospherical geometry) in hyperbolic $3$space.
Especially, we give a generic classification of singularities
of such surfaces.
As a consequence, we can say that such a class of surfaces has
quite a rich geometric structure.
Item Type:  Preprint 

Additional Information:  60 

Uncontrolled Keywords:  Hyperbolic $3$space,
Horosphere, Horospherical geometry, Horoflat surfaces, Singularities 

Subjects:  53xx DIFFERENTIAL GEOMETRY 

ID Code:  1688 

