Dual Darboux Frame of a Timelike Ruled Surface and Darboux Approach to Mannheim Offsets of Timelike Ruled Surfaces

Details Dual Darboux Frame of a Timelike Ruled Surface and Darboux Approach to Mannheim Offsets of Timelike Ruled Surfaces Dual Darboux Frame of a Timelike Ruled Surface and Darboux Approach to Mannheim Offsets of Timelike Ruled Surfaces

2011-08-30

arxiv.org/abs/1108.6076v2

Mathematics

Differential Geometry

14 pages

Scientific paper

In this paper, we give the dual geodesic trihedron(dual Darboux frame) of a timelike ruled surface. Then, we study Mannheim offsets of timelike ruled surfaces in dual Lorentzian space. By the aid of the E. Study Mapping, we consider the timelike ruled surfaces as dual hyperbolic unit spherical curves and define the Mannheim offsets of the timelike ruled surfaces by means of dual Darboux frame. We obtain the relationships between the invariants of Mannheim timelike offset surfaces. Furthermore, we give the conditions for these surface offset to be developable.

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