The Intersection of Two Ruled Surfaces Corresponding to Spherical Indicatrix Curves on the Unit Dual Sphere

In this study, we first investigate the intersection of two different ruled surfaces in R^3 for two different tangential spherical indicatrix curves on DS^2 using the E. Study mapping. The conditions for the intersection of these ruled surfaces in R^3 are expressed by theorems with bivariate functions. Secondly, considering two different principal normal spherical indicatrix curves on DS^2, we examine the intersection of two different ruled surfaces in R^3 by using E. Study mapping. Similarly, the conditions for the intersection of these ruled surfaces in R^3 are indicated by theorems with bivariate functions. Thirdly, using E. Study mapping, we explore the intersection of two different ruled surfaces in R^3 by considering two different binormal spherical indicatrix curves on DS^2. Likewise, the conditions for the intersection of these ruled surfaces in R^3 are denoted by theorems with bivariate functions. Fourthly, considering two different pole spherical indicatrix curves on DS^2, we study the intersection of two different ruled surfaces in R^3 by using E. Study mapping. In the same way, the conditions for the intersection of these ruled surfaces in R^3 are specified by theorems with bivariate functions. Finally, we provide some examples that support the main results.