Timelike ruled surfaces with spacelike rulings in IR13

Abstract

In this paper, the well known theorems given by Bonnet and Chasles in the 3-dimensional Euclidean space are proved for a timelike ruled surface which obtained by a spacelike straight line which moves along a timelike curve. Gaussian curvature function of the ruled surface and some theorems related to this function are expressed. A differential equation of geodesic curves on the surface is obtained. The relationship between the geodesic curvature k(g) and normal curvature k(n) of the timelike base curve are also given. Finally, a new classification for the maximal timelike ruled surfaces with spacelike rulings different from the literature has been found.