The horospherical geometry of surfaces in Hyperbòlic 4-space
Shyūichi Izumiya, Donghe Pei, M. C. Romero Fuster · EPrints - Department of Mathematics, Hokkaido University · 2004
We study some geometrical properties associated to the contacts of surfaces with hyperhorospheres in Ht ( -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.