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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)
  • Received : 2012.09.07
  • Published : 2013.09.30

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

Acknowledgement

Supported by : National Research Foundation of Korea (NRF)

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