The horospherical geometry of surfaces in hyperbolic 4-space |
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| Authors: | Shyuichi Izumiya Donghe Pei María del Carmen Romero Fuster |
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| Institution: | (1) Department of Mathematics, Hokkaido University, 060-0810 Sapporo, Japan;(2) Department of Mathematics, North East Normal University, 130024 Changchun, P.R. China;(3) Departament de Geometria i Topologia, Universitat de València, 46100 Burjassot (València), Spain |
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| Abstract: | 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.
Work partially supported by Grant-in-Aid for Scientific Research, JSPS, No. 12874007.
Work partially supported by Grant-in-Aid for Scientific Research, JSPS, No. 12000266.
Work partially supported by DGCYT grant no. BFM2003-02037. |
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