The horospherical geometry of surfaces in Hyperbolic 4-space

Abstract

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