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

摘要

In this paper, we introduce the dual geodesic trihedron (dual Darboux frame)of a timelike ruled surface. By the aid of the E. Study Mapping, we considertimelike ruled surfaces as dual hyperbolic spherical curves and define theMannheim offsets of timelike ruled surfaces by means of dual Darboux frame. Weobtain the relationships between invariants of Mannheim timelike surfaceoffsets. Furthermore, we give the conditions for these surface offsets to bedevelopable.