Chord Properties of Some Special Curves in Euclidean Space

Year 2020, Volume: 12 Issue: 1, 39 - 44, 29.06.2020

Emre Öztürk Yusuf Yaylı

Abstract

In this paper, we define some special curves through the chord that combines two different points of the curve on it, and we examine relations of these curves each other. Especially, these curves have been characterized by their unit tangent vector field itself with symmetric and skew symmetric matrix. Moreover, we show that these curves are the geodesics of the isoparametric surfaces such as spheres, right circular cylinders and spherical cylinders.                                                                                                                                                                                                                     

Keywords

Curve with constant curvature, isoparametric surface, .

References

• Aminov, Y., Differential Geometry and Topology of Curves, Gordon and Breach Science Publishers imprint, London, 2003.
• Chen, B.Y., Kim, D.S., Kim, Y.H., New characterizations of W-Curves, Publ. Math. Debrecen 69 / 4(2006), 457-472.
• Kim, D.S., Kim, Y.H.,New characterizations of spheres, cylinders and W-curves, Linear Algebra and Its Applications 432 (2010), 3002-3006.
• Kim, Y.H., Lee, K.E., Surfaces of Euclidean 4-Space Whose Geodesics are W-Curves, Nihonkai Math. J., 4(1993), 221-232.
• Munteanu, M.I., Nistor, A.I., The classification of Killing magnetic curves in S2× R , Journal of Geometry and Physics 62(2012), 170-182.
• Öztürk, E., Yaylı, Y., W-Curves In Lorentz-Minkowski Space, Mathematical Sciences and Applications E-Notes, 5 / 2(2017), 76–88.
• Öztürk, E., Yaylı, Y., Elementary Approaches on De Sitter Space, Mathematical Sciences and Applications E-Notes, 7 / 2 (2019), 183-190.
• Walrave, J., Curves and Surfaces in Minkowski Space, Ph.D. Dissertation, K.U.Leuven, 1995.