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CURVES ON THE UNIT 3-SPHERE S3(1) IN EUCLIDEAN 4-SPACE ℝ4
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 Title & Authors
CURVES ON THE UNIT 3-SPHERE S3(1) IN EUCLIDEAN 4-SPACE ℝ4
Kim, Chan Yong; Park, Jeonghyeong; Yorozu, Sinsuke;
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 Abstract
We show many examples of curves on the unit 2-sphere in and the unit 3-sphere in . 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;
 Language
English
 Cited by
 References
1.
Yu. Aminov, Differential Geometry and Topology of Curves, Gordon and Breach Science Publishers, Amsterdam, 2000.

2.
Yu. Aminov, The Geometry of Submanifolds, Gordon and Breach Science Publishers, Amsterdam, 2001.

3.
H. Balgetir, M. Bektas, and J.-I. Inoguchi, Null Bertrand curves in Minkowski 3-space and their characterizations, Note Mat. 23 (2004), no. 1, 7-13.

4.
P. A. Blaga, Lectures on the Differential Geometry of Curves and Surfaces, Napoca Press, 2005.

5.
M. P. do Carmo, Differential Geometry of Curves and Surfaces, Prentice-Hall, Englewood Cliffs, NJ. 1976.

6.
N. Ekmekci and K. Ilarslan, On Bertrand curves and their characterization, Differ. Geom. Dyn. Syst. 3 (2001), no. 2, 17-24.

7.
C.-C. Hsiung, A First Course in Differential Geometry, International Press, Cambridge, MA. 1997.

8.
S. Izumiya and N. Takeuchi, Generic properties of helices and Bertrand curves, J. Geom. 74 (2002), no. 1-2, 97-109. crossref(new window)

9.
P. Lucas and J. A. Ortega-Yagues, Bertrand curves in the three-dimensional sphere, J. Geom. Phys. 62 (2012), no. 9, 1903-1914. crossref(new window)

10.
H. Matsuda and S. Yorozu, Notes on Bertrand curves, Yokohama Math. J. 50 (2003), no. 1-2, 41-58.

11.
R. S. Millman and G. D. Parker, Elements of Differential Geometry, Prentice-Hall Inc, 1977.

12.
J. Monterde, Curves with constant curvature ratios, Bol. Soc. Mat. Mexicana (3) 13 (2007), no. 1, 177-186.

13.
L. R. Pears, Bertrand curves in Riemannian space, J. London Math. Soc. (1935), no. 2, 180-183.

14.
W. K. Schief, On the integrability of Bertrand curves and Razzaboni surfaces, J. Geom. Phys. 45 (2003), no. 1-2, 130-150. crossref(new window)