# 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);

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## Abstract

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.

Item Type: Preprint Legendrian dualities, spacelike hypersurfaces, Hyperbolic space, de Sitter space, Lorentz-Minkowski space. 53-xx DIFFERENTIAL GEOMETRY 2054