Israel Journal of Mathematics

, Volume 154, Issue 1, pp 361–379 | Cite as

The horospherical geometry of surfaces in hyperbolic 4-space

  • Shyuichi Izumiya
  • Donghe Pei
  • María del Carmen Romero Fuster


We study some geometrical properties associated to the contacts of surfaces with hyperhorospheres inH + 4 (−1). We introduce the concepts of osculating hyperhorospheres, horobinormals, horoasymptotic directions and horospherical points and provide conditions ensuring their existence. We show that totally semiumbilical surfaces have orthogonal horoasymptotic directions.


Fundamental Form Generic Surface Normal Field Spacelike Surface Curvature Ellipse 
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Copyright information

© The Hebrew University 2006

Authors and Affiliations

  • Shyuichi Izumiya
    • 1
  • Donghe Pei
    • 2
  • María del Carmen Romero Fuster
    • 3
  1. 1.Department of MathematicsHokkaido UniversitySapporoJapan
  2. 2.Department of MathematicsNorth East Normal UniversityChangchunP.R. China
  3. 3.Departament de Geometria i TopologiaUniversitat de ValènciaBurjassot (València)Spain

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