[KSCI] Korea Science Citation Index Service

http://dx.doi.org/10.4134/CKMS.c160024

FOCAL SURFACES AND EVOLUTES OF CURVES IN HYPERBOLIC SPACE

Hayashi, Ryota (Department of Mathematics Hokkaido University)
Izumiya, Shyuichi (Department of Mathematics Hokkaido University)
Sato, Takami (Shiseikan Elementary School)

Publication Information

Communications of the Korean Mathematical Society / v.32, no.1, 2017 , pp. 147-163 More about this Journal

Abstract

We define de Sitter focal surfaces and hyperbolic focal surfaces of hyperbolic space curves. As an application of the theory of unfoldings of function germs, we investigate the singularities of these surfaces. For characterizing the singularities of these surfaces, we discover a new hyperbolic invariants and investigate the geometric meanings.

Keywords

hyperbolic space; hyperbolic space curves; focal surfaces; evolutes;

Citations & Related Records

Reference

1	J. W. Bruce and P. J. Giblin, Curves and Singularities, Second Edition, Cambridge University press, 1992.
2	S. Izumiya, D.-H. Pei, and T. Sano, Horospherical surfaces of curves in hyperbolic space, Publ. Math. Debrecen 64 (2004), no. 1-2, 1-13.
3	S. Izumiya and T. Sato, Lightlike hypersurfaces along spacelike submanifolds in Minkowski space-time, J. Geom. Phys. 71 (2013), 30-52. DOI