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

摘要

In this paper, we define dual geodesic trihedron(dual Darboux frame) of aspacelike ruled surface. Then, we study Mannheim offsets of spacelike ruledsurfaces in dual Lorentzian space by considering the E. Study Mapping. Werepresent spacelike ruled surfaces by dual Lorentzian unit spherical curves anddefine Mannheim offsets of the spacelike ruled surfaces by means of dualDarboux frame. We obtain relationships between the invariants of Mannheimspacelike offset surfaces and offset angle, offset distance. Furthermore, wegive conditions for these surface offsets to be developable.