Communications of the
Korean Mathematical Society
CKMS

ISSN(Print) 1225-1763 ISSN(Online) 2234-3024

Article

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Commun. Korean Math. Soc. 2017; 32(1): 147-163

Online first article October 12, 2016      Printed January 31, 2017

https://doi.org/10.4134/CKMS.c160024

Copyright © The Korean Mathematical Society.

Focal surfaces and evolutes of curves in hyperbolic space

Ryota Hayashi, Shyuichi Izumiya, and Takami Sato

Hokkaido University, Hokkaido University, Chuoku Minami 3 Nishi 7

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

MSC numbers: Primary 53A25; Secondary 58K35