On the Line Congruences

Abstract

The purpose of this paper is to find the quantities and surfaces of a line congruence via examining it in the dual space and to represent the results more appropriately for computational approximations. For this, we take mainly two-dual parameter motion on the dual unit sphere (DUS) so, we get a line congruence corresponding this motion by a new method. Thus, the equations of the developable surfaces, the principal surfaces, the focal surfaces and the center surface of the line congruence are found by coordinate functions. The results are illustrated by examples.