A different view of the tube surface in Minkowski 3-space $E_{1}^{3}$

Abstract

A basic goal of this paper is to study the tube surface with a null Cartan curve with respect to the Bishop frame in Minkowski 3-space $E_{1}^{3}$ and to compute some geometric features for this kind of the tube surface such as, the first and the second fundamental forms, the mean and the Gaussian curvatures. Furthermore, using the mean curvature $H$ and the Gaussian curvature $K$, we investigate $\Omega(K,H)-$ surface condition of the tube surface with the null Cartan curve due to the Bishop frame in Minkowski 3-space $E_{1}^{3}$.