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 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.