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

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

REVISTA MATEMATICA IBEROAMERICANA, cilt.28, sa.2, ss.371-400, 2012 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 28 Sayı: 2
  • Basım Tarihi: 2012
  • Doi Numarası: 10.4171/rmi/681
  • Dergi Adı: REVISTA MATEMATICA IBEROAMERICANA
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.371-400
  • İstanbul Üniversitesi Adresli: Evet

Özet

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.