Another application of Smarandache based ruled surfaces with the Darboux vector according to Frenet frame in $E^{3}$

Year 2023, Volume: 72 Issue: 4, 880 - 906, 29.12.2023

Süleyman Şenyurt , Davut Canlı , Elif Çan , Sümeyye Gür Mazlum

https://doi.org/10.31801/cfsuasmas.1151064

Cited By: 4

https://izlik.org/JA98MS45KW

Abstract

In 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.

Keywords

Smarandache curve , ruled surfaces , mean curvature , Gaussian curvature , Viviani's curve

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