Curves on the unit 3-sphere $S^3(1)$ in Euclidean 4-space $\mathbb{R}^4$
Bull. Korean Math. Soc. 2013 Vol. 50, No. 5, 1599-1622
Printed September 1, 2013
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
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