Some results on space-like line congruences and their space-like parameter ruled surfaces

Abstract

Using dual vectors, space-like ruled surfaces was introduced in [2]. In this paper, we define space-like line congruence and their space-like parameter ruled surfaces ${mathbf R_11(t)}$ and ${mathbf R21(t)}$ of $R^1_3$. Then, by choosing space-like parameter ruled surfaces as space-like principle ruled surfaces, we obtain some relations among the magnitudes of space-like ruled surfaces ${mathbf R_1(t)}$, ${mathbf R11(t)}$.