Bulletin of the
Korean Mathematical Society
BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

Article

HOME ALL ARTICLES View

Bull. Korean Math. Soc. 2013; 50(5): 1599-1622

Printed September 1, 2013

https://doi.org/10.4134/BKMS.2013.50.5.1599

Copyright © The Korean Mathematical Society.

Curves on the unit 3-sphere $S^3(1)$ in Euclidean 4-space $\mathbb{R}^4$

Chan Yong Kim, JeongHyeong Park, and Sinsuke Yorozu

Sungkyunkwan University, Sungkyunkwan University, Miyagi University of Education

Abstract

We show many examples of curves on the unit 2-sphere $S^2 (1)$ in $\mathbb{R}^3$ and the unit 3-sphere $S^3 (1)$ in $\mathbb{R}^4$. We study whether its curves are Bertrand curves or spherical Bertrand curves and provide some examples illustrating the resultant curves.

Keywords: spherical curve, Bertrand curve, spherical Bertrand curve

MSC numbers: 53A04