Ruled Surfaces with Time-Like Rulings

Abstract

In this article, a new type of ruled surfaces in a Lorentz 3-space R-1(3) is obtained by a strictly connected time-like oriented line moving with Frenet's frame along a space-like curve. These surfaces are classified into time-like and space-like surfaces. The wellknown theorems due to Bonnet and Chasles in the 3-dimensional Euclidean space are proved for a time-like ruled surface. (c) 2005 Published by Elsevier Inc.