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

Asayama M., Izumiya S., Tamaoki A., Yildirim H.

REVISTA MATEMATICA IBEROAMERICANA, vol.28, no.2, pp.371-400, 2012 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 28 Issue: 2
  • Publication Date: 2012
  • Doi Number: 10.4171/rmi/681
  • Journal Indexes: Science Citation Index Expanded, Scopus
  • Page Numbers: pp.371-400


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-Robecheyski 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.