The Pitch and the Angle of Pitch of a Closed Piece of Ruled Surface in R31

It is well known that in the Euclidean space R3, the pitch and the angle of pitch on a ruled surface whose directrix curve is periodic can be given [6]. On the other hand, since there is no periodic timelike curve in the Minkowsky space R31, we give similar formulas on a closed piece of a ruled surface which is obtained by restricting the directrix curve of a ruled surface to a closed interval [a,b] contained in the domain of the directrix curve. Since the directrix curve is periodic spacelike, the formulas are the same in the Euclidean case when the length of the closed interval is equal to the period of the curve