On The Parallel Ruled Surfaces With B-Darboux Frame

In this work, the geometric properties of parallel ruled surfaces associated with the B-Darboux frame (BDF) in $E%%TCIMACRO{\U{b3}}%%BeginExpansion{{}^3}%%EndExpansion$ are introduced. Firstly, these surfaces are presented, and their main characteristic properties, such as developability, stress points and dispersion parameter, are analyzed. The paper presents a comprehensive analysis of how these surfaces are constructed and describes the conditions under which they preserve certain geometrical properties with the B-Darboux frame in Euclidean 3-space. These results contribute to a much better understanding of the theory of parallel ruled surfaces (PRS) with regard to the B-Darboux frame and provide insights into potential applications in various fields of geometry and mathematical modeling.