On the Developable Mannheim Offsets of Timelike Ruled Surfaces

Abstract

In this paper, using the classifications of timelike and spacelike ruled surfaces, we study the Mannheim offsets of timelike ruled surfaces in Minkowski 3-space. Firstly, we define the Mannheim offsets of a timelike ruled surface by considering the Lorentzian casual character of the offset surface. We obtain that the Mannheim offsets of a timelike ruled surface may be timelike or spacelike. Furthermore, we characterize the developable of Mannheim offset of a timelike ruled surface by the derivative of the conical curvature of the directing cone.