Characterization of the Evolute Offset of Ruled Surfaces with B-Darboux Frame

Abstract

In this paper, we first introduce the evolute offset of non-cylindrical ruled surfaces with B-Darboux frame in Euclidean 3-space. Then some geometric properties of this evolute offset of non-cylindrical ruled surface are studied. That is, we examine the striction curve, distribution parameter, orthogonal trajectory of evolute offset of ruled surfaces in terms of B-Darboux frame of given ruled surfaces, and we study the developability of ruled surface generated by B-Darboux vectors in three-dimensional Euclidean space.

Keywords

• B-Darboux Frame
• Curvatures
• Evolute Offset
• Ruled Surface

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