Emre ÖZTÜRK, Yusuf YAYLI

Chord Properties of Some Special Curves in Euclidean Space

ISSN: 2148-1830
Yayın Aralığı: 2
Başlangıç: 2013
Yayıncı: MATEMATİKÇİLER DERNEĞİ

In this paper, we define some special curves through the chord that combines two different points ofthe 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 thatthese curves are the geodesics of the isoparametric surfaces such as spheres, right circular cylinders and sphericalcylinders.

PDF

___

[1] Aminov, Y., Differential Geometry and Topology of Curves, Gordon and Breach Science Publishers imprint, London 2003. 1
[2] Chen, B.Y., Kim, D.S., Kim, Y.H., New characterizations of W-Curves, Publ. Math. Debrecen 69(4)(2006), 457-472. 1
[3] Kim, D.S., Kim, Y.H., New characterizations of spheres, cylinders and W-curves, Linear Algebra and Its Applications 432 (2010), 3002-3006. 1, 1, 1, 2
[4] Kim, Y.H., Lee, K.E., Surfaces of Euclidean 4-Space Whose Geodesics are W-Curves, Nihonkai Math. J., 4(1993), 221-232. 1
[5] Munteanu, M.I., Nistor, A.I., The classification of Killing magnetic curves in S 2 × R, Journal of Geometry and Physics 62(2012), 170-182. 2
[6] Ozt ¨ urk, E., Yaylı, Y., ¨ W-Curves In Lorentz-Minkowski Space, Mathematical Sciences and Applications E-Notes, 5(2)(2017), 76–88. 1, 1
[7] Ozt ¨ urk, E., Yaylı, Y., ¨ Elementary Approaches on De Sitter Space, Mathematical Sciences and Applications E-Notes, 7(2) (2019), 183-190. 1
[8] Walrave, J., Curves and Surfaces in Minkowski Space, Ph.D. Dissertation, K.U.Leuven, 1995. 1