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http://dx.doi.org/10.4134/BKMS.2013.50.5.1599

CURVES ON THE UNIT 3-SPHERE S3(1) IN EUCLIDEAN 4-SPACE ℝ4  

Kim, Chan Yong (Department of Mathematics Sungkyunkwan University)
Park, Jeonghyeong (Department of Mathematics Sungkyunkwan University)
Yorozu, Sinsuke (Department of Mathematics Miyagi University of Education)
Publication Information
Bulletin of the Korean Mathematical Society / v.50, no.5, 2013 , pp. 1599-1622 More about this Journal
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;
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