- Turkish Journal of Mathematics
- Vol: 42 Issue: 4
- A study of the tubular surfaces constructed by the spherical indicatrices in Euclidean $3-$space
A study of the tubular surfaces constructed by the spherical indicatrices in Euclidean $3-$space
Authors : Fatma Ateş, Erdem Kocakuşakli, Ismail Gök, Yusuf Yayli
Pages : 1711-1725
View : 15 | Download : 4
Publication Date : 9999-12-31
Article Type : Makaleler
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. (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