The horospherical geometry of surfaces in hyperbolic 4-space

6533b839fe1ef96bd12a58ac

RESEARCH PRODUCT

The horospherical geometry of surfaces in hyperbolic 4-space

M. C. Romero-fuster Shyuichi Izumiya D. Pei

subject

Normal field General Mathematics Geometry Algebra over a field Space (mathematics)Mathematics Osculating circle

description

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.

year	journal	country	edition	language
2006-12-01	Israel Journal of Mathematics

https://doi.org/10.1007/bf02773613

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