Characterizations of Curves According to Frenet Frame in Euclidean 3-Space

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Turkish Journal of Mathematics and Computer Science
Volume:11 Issue:1
Characterizations of Curves According to Frenet Frame in Euclidean 3-Space

Characterizations of Curves According to Frenet Frame in Euclidean 3-Space

Authors : Osman ÇAKIR, Süleyman ŞENYURT

Pages : 48-52

View : 35 | Download : 13

Publication Date : 2019-06-30

Article Type : Research Paper

Abstract :In this paper, we investigate the conditions of being an harmonic curve and research differential equations characterizing any differentiable curve in Euclidean 3-space. By means of the Laplacian image of the mean curvature vector field of a curve, it is stated which type of harmonic the curve is. Then we write the theorems related to the characterization of the curves and proved these theorems. When the differentiable curve, used throughout this paper, is specifically replaced to the unit speed curve then it is seen that the results coincide with the study [4]. In addition we elucidate the characterizations of helix as an example.
Keywords : regular curve, connection, mean curvature, biharmonic, differential equation

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