  In this paper, we obtain the characterizations of Mannheim offsets of the
timelike ruled surface with spacelike rulings in dual Lorentzian space. We give
the relations between terms of their integral invariants and also we give the
new characterization of the Mannheim offsets of developable timelike ruled
surface. Moreover, we obtain the relationships between the area of projections
of spherical images for Mannheim offsets of timelike ruled surfaces and their
integral invariants.
