Ruled surfaces with timelike rulings

In this article, a new type of ruled surfaces in a Lorentz 3-space R-1(3) is obtained by a strictly connected timelike oriented line moving with Frenet's frame along a spacelike curve. These surfaces are classified into timelike and spacelike surfaces. The well-known theorems due to Bonnet and Chasles in the 3-dimensional Euclidean space are proved for a timelike ruled surface. For developable and maximal timelike ruled surfaces [Minimal Surfaces of the 3-Dimensional Minkowski Space, World Scientific Publishing, Singapore, 1990, p. 344], some results are obtained. The relation between geodesic curvature, normal curvature and the curvature of a general curve on a timelike ruled surface is derived. (C) 2002 Published by Elsevier Inc.