On the integral invariants of a time-like ruled surface

Abstract

In this study, we discuss the dual Lorentzian spherical motions and calculate the real integral invariants of a closed time-like ruled surfaces in $R_1^3$. Then, we define the dual angle of pitch of a closed time-like ruled surface, and give a relation between the dual Steiner vector of the dual spherical motion and dual angle of pitch of the time-like ruled surface. Finally, we obtain a relation between the dual angle of pitch and the real integral invariants of time-like ruled surface.