Yİ-DARBOUX SLANT HELICES ON SURFACES

In this study, a new class of surface curves, namely Yi-Darboux slant helices, is investigated. The conditions under which a surface curve is a iY-Darboux slant helix with respect to the Osculating Darboux (OD), Normal Darboux (ND), and Rectifying Darboux (RD) frames are established, and several characterizations are obtained. In particular, necessary and sufficient conditions are derived in terms of the curvature functions associated with these frames. Furthermore, relationships between iY-Darboux slant helices and classical helices and slant helices are established for special surface curves, including geodesics, asymptotic curves, and lines of curvature. Concrete examples on conical and cylindrical surfaces are also presented to illustrate the theoretical results.