The tangent conoids family which depends on the ruled surface

In this study, a new congruence [A**] has been defined by putting a tangent right conoid on each line of a ruled surface $(A_1(s))$ of a line congruence [A]. Then, by considering special case of the congruence [A**] which has been defined in the previous part, the concepts of tangent congruence, drall and the relation among Blaschke vectors of Blaschke trihedrons, having common line $A_0$, has been examined for this special case. At the end of this study, the concept of tangent congruence for some special congruences has been examined

On the closed motions and closed space-like ruled surfaces

The theorems about closed motion in Euclidean space is given in [2] and [3]. In this paper, using the real Steiner rotation and translation vectors, we have given some theorems about the real pitch and the real angle of pitch which are the integral invariants of the closed space-like ruled surfaces. Taking a space-like line x in Frenet trihedron {t,n,b}, the real angle of pitch of space-like ruled surface, which is drawn by the space- like line x, is calculated by the .real angle of pitchs of space-like ruled surfaces those are drawn by the space-like lines t and b. Then, we give some theorems about dral and harmonic curvature in $R_1^3$ .The theorems about closed motion in Euclidean space is given in [2] and [3]. In this paper, using the real Steiner rotation and translation vectors, we have given some theorems about the real pitch and the real angle of pitch which are the integral invariants of the closed space-like ruled surfaces. Taking a space-like line x in Frenet trihedron {t,n,b}, the real angle of pitch of space-like ruled surface, which is drawn by the space- like line x, is calculated by the .real angle of pitchs of space-like ruled surfaces those are drawn by the space-like lines t and b. Then, we give some theorems about dral and harmonic curvature in $R_1^3$