On the Invariants of Mannheim Offsets of Timelike Ruled Surfaces with Timelike Rulings

In this study, we give dual characterizations for Mannheim offsets of timelike ruled surfaces with timelike rulings in terms of their integral invariants. Also, we give new characterization for the Mannheim offsets of developable timelike ruled surfaces. We show that if the offset surfaces are developable then the striction lines of surfaces are Mannheim curves. Moreover, we obtain relationships between areas of projections of spherical images for Mannheim offsets of timelike ruled surfaces and their integral invariants.