Timelike tubes with Darboux frame in Minkowski 3-space

Abstract

In this study, we define a timelike tube around a spacelike curve with timelike binormal by taking Darboux frame instead of Frenet frame in Minkowski 3-space. Subsequently, we compute the Gaussian curvature, the mean curvature, and the second Gaussian curvature of timelike tube with Darboux frame and obtained some characterizations for special curves on this timelike tube around a spacelike curve with timelike binormal.