On the Developable of Mannheim Offsets of Timelike Ruled Surfaces in Minkowski 3-Space

Details On the Developable of Mannheim Offsets of Timelike Ruled Surfaces in Minkowski 3-Space On the Developable of Mannheim Offsets of Timelike Ruled Surfaces in Minkowski 3-Space

2009-06-11

arxiv.org/abs/0906.2077v5

Mathematics

Differential Geometry

11 pages

Scientific paper

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.

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