Alkan, AkinKocayigit, HuseyinAydin, Tuba Agirman2026-02-282026-02-2820251844-95812068-3049https://doi.org/10.46939/J.Sci.Arts-25.2-a10https://hdl.handle.net/20.500.12403/6210In this article, the differential equation characterizations for D-i-Darboux slant helices given with the help of three new orthogonal frames are introduced for the curves lying on a surface. These moving frames, obtained based on the Darboux frame, are called Osculating Darboux Frame, Normal Darboux Frame, and Rectifying Darboux Frame, respectively.eninfo:eu-repo/semantics/openAccessDarboux slant helixSlant HelixDarboux FrameOD-FrameND-FrameRD-FrameArticle232533610.46939/J.Sci.Arts-25.2-a10WOS:001531580300010Q4