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

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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Turkish Journal of Mathematics and Computer Science-Cover

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

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