Slant geometry of spacelike hypersurfaces in the lightcone


Izumiya S., Yildirim H.

JOURNAL OF THE MATHEMATICAL SOCIETY OF JAPAN, vol.63, no.3, pp.715-752, 2011 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 63 Issue: 3
  • Publication Date: 2011
  • Doi Number: 10.2969/jmsj/06330715
  • Journal Name: JOURNAL OF THE MATHEMATICAL SOCIETY OF JAPAN
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.715-752
  • Keywords: Legendrian dualities, spacelike hypersurfaces, lightcone, Lorentz-Minkowski space, HOROSPHERICAL GEOMETRY, LEGENDRIAN DUALITIES, HYPERBOLIC SPACE, PSEUDO-SPHERES, SURFACES, CONE
  • Istanbul University Affiliated: Yes

Abstract

In this paper, we consider one-parameter families of new extrinsic differential geometries on spacelike hypersurfaces in the lightcone. These geometries are constructed by applying two of one-parameter families of Legendrian dualities between pseudo-spheres in Lorentz-Minkowski space. These Legendrian dualities have been recently given as a part of extensions of the mandala of Legendrian dualities in the previous research of the authors.