Slant Geometry of Spacelike Hypersurfaces in Hyperbolic space and de Sitter space
Preprint Series # 962
Asayama, Mikuri and Izumiya, Shyuichi and Tamaoki, Aiko and Yildirim, Handan Slant Geometry of Spacelike Hypersurfaces in Hyperbolic space and de Sitter space. (11 May 2010);
We consider a one-parameter family of new extrinsic differential geometries
on hypersurfaces in Hyperbolic space. Recently, the second author and his collaborators have
constructed a new geometry which is called horospherical geometry on Hyperbolic space.
There is another geometry which is the famous Gauss-Boryay-Robechevski geometry (i.e., the
hyperbolic geometry) on Hyperbolic space. The slant geometry is a one-parameter family of geometries which
connect these two geometries. Moreover, we construct a one-parameter family of geometries on
spacelike hypersurfaces in de Sitter space.
|Uncontrolled Keywords:||Legendrian dualities, spacelike hypersurfaces, Hyperbolic space, de Sitter space,
|Subjects:||53-xx DIFFERENTIAL GEOMETRY|