Revista Matemática Iberoamericana


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Volume 28, Issue 2, 2012, pp. 371–400
DOI: 10.4171/rmi/681

Published online: 2012-04-22

Slant geometry of spacelike hypersurfaces in hyperbolic space and de Sitter space

Mikuri Asayama[1], Shyuichi Izumiya[2], Aiko Tamaoki[3] and Handan Yıldırım[4]

(1) Hokkaido University, Sapporo, Japan
(2) Hokkaido University, Sapporo, Japan
(3) Hokkaido University, Sapporo, Japan
(4) Istanbul University, Vezneciler/istanbul, Turkey

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–Bolyai–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.

Keywords: Legendrian dualities, spacelike hypersurfaces, hyperbolic space, de Sitter space, Lorentz–Minkowski space

Asayama Mikuri, Izumiya Shyuichi, Tamaoki Aiko, Yıldırım Handan: Slant geometry of spacelike hypersurfaces in hyperbolic space and de Sitter space. Rev. Mat. Iberoamericana 28 (2012), 371-400. doi: 10.4171/rmi/681