We consider the rectilinear congruence T generated by the tangents to a one parameter family of geodesics on a space-like surface S1 in the Minkowski 3-space E13, having S1 as one of its focal surfaces. We prove that ...We consider the rectilinear congruence T generated by the tangents to a one parameter family of geodesics on a space-like surface S1 in the Minkowski 3-space E13, having S1 as one of its focal surfaces. We prove that the two families of torsal surfaces of T touch the second focal surface S2 along the net of orthogonal parametric curves if and only if S1 is developable. We also obtain the necessary and sufficient condition for the correspondence between the points of S1 and S2 at the same rays preserving the net of asymptotic curves. At last, we investigate the orthogonal surface S of T. We proved that the correspondence between S1 and S2 preserves the net of asymptotic curves if S is maximal in E13.展开更多
基金Specialized Research Fund for the Doctoral Program of Higher Education (No.20050141011)
文摘We consider the rectilinear congruence T generated by the tangents to a one parameter family of geodesics on a space-like surface S1 in the Minkowski 3-space E13, having S1 as one of its focal surfaces. We prove that the two families of torsal surfaces of T touch the second focal surface S2 along the net of orthogonal parametric curves if and only if S1 is developable. We also obtain the necessary and sufficient condition for the correspondence between the points of S1 and S2 at the same rays preserving the net of asymptotic curves. At last, we investigate the orthogonal surface S of T. We proved that the correspondence between S1 and S2 preserves the net of asymptotic curves if S is maximal in E13.
