2026-10-23T22:57:18Zhttps://gumushane-rdlopen.rawdatalibrary.net/oai/request

oai:gumushane-rdlopen.rawdatalibrary.net:gumushane/145642026-10-22T11:37:14Zopenairedrivercom_gumushane_10000col_gumushane_10001

ANOTHER APPLICATION OF SMARANDACHE BASED RULED SURFACES WITH THE DARBOUX VECTOR ACCORDING TO FRENET FRAME IN E3Şenyurt, SüleymanCanli, DavutÇan, ElifMazlum, Sümeyye GürGaussian curvaturemean curvatureruled surfacesSmarandache curveViviani’s curveIn this study, we first define the Smarandache curves derived from the Frenet vectors and the Darboux vector of any curve. Then, we construct new ruled surfaces along these Smarandache curves with the direction vectors obtained from the Frenet vectors and the Darboux vector, and give the equations of these surfaces. In addition, we calculate the Gaussian and mean curvatures of these surfaces separately and present the conditions to be minimal and developable for these surfaces. Finally, as an example, we obtain ruled surfaces whose base curves are Viviani’s curves and plot the graphics of these surfaces.Ankara University Faculty of Science2023Articlehttps://rdlopen.rawdatalibrary.net/r/gumushane/14564https://doi.org/10.31801/cfsuasmas.11510641303-5991enCommunications Faculty of Sciences University of Ankara Series A1 Mathematics and Statisticsinfo:eu-repo/semantics/openAccessinfo:eu-repo/semantics/articlehttps://gumushane-rdlopen.rawdatalibrary.net/tr/items/gumushane/14564