Some characterizations of translation surface generated by a non-null curve and a curve on a spacelike surface in Minkowski 3-space

Abstract

In this paper, we study translation surfaces generated by a non-null curve in Minkowski 3-space and a curve lying on a spacelike surface in Minkowski $3$-space and obtain necessary and sufficient conditions for such surfaces to be flat or minimal. Further we obtain normal curvature, geodesic curvature and geodesic torsion of the generating curves and find necessary and sufficient conditions for these curves to be geodesic, asymptotic line and line of curvature. Finally we study some special cases of such translation surfaces according to the angle between the normal of the translation surface and the normals of the generating curves.