In this study, considering two different curves on the unit dual sphere, 〖DS〗^2, we investigate the intersection of two different ruled surfaces in R^3 by using E. Study mapping. The conditions for the intersection of these ruled surfaces in R^3 are expressed by theorems with bivariate functions. Finally, some examples are given to support the main results.

In this article, firstly, the intersection of two ruled surfaces corresponding to two different curves on S_1^2 is investigated. The conditions for the intersection of these ruled surfaces in R_1^3 are expressed by theorems with bivariate functions. Then, the intersection of two ruled surfaces corresponding to two different curves on H^2 is examined. Similarly, the conditions for the intersection of these ruled surfaces in R_1^3 are shown by some illustrative theorems with bivariate functions. Finally, some examples are given to support the main results.

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.

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