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

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 γ on a surface is defined by the property that its fundamental coefficients satisfy Eq. (3.7) along the curve γ . At the end of this article, we exemplify these curves on the tubular surfaces with their figures using the program Mathematica.