A study of the tubular surfaces constructed by the spherical indicatrices in Euclidean $3-$space

Authors : Fatma ATEŞ, Erdem KOCAKUŞAKLI, İsmail GÖK, Yusuf YAYLI

Pages : 1711-1725

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Publication Date : 0000-00-00

Article Type : Research Paper

Abstract :A basic goal of this paper is to investigate the tubular surface constructed by the spherical indicatrices of any spatial curve in the Euclidean $3-$ space. This kind of tubular surface is designed for the alternative moving frame $\{N,C,W\}$ in conjunction with finding a relationship between the tubular surfaces and their special curves, such as geodesic curves, asymptotic curves, and minimal curves. The minimal curve $\gamma $ on a surface is defined by the property that its fundamental coefficients satisfy Eq. insert ignore into journalissuearticles values(3.7); along the curve $\gamma $. At the end of this article, we exemplify these curves on the tubular surfaces with their figures using the program Mathematica.
Keywords : Tubular surface, indicatrix curve, minimal curve