Another application of Smarandache based ruled surfaces with the Darboux vector according to Frenet frame in $E^{3}$-Reference-Cited by-同舟云学术

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

Published:2023-07-08 Issue:4 Volume:72 Page:880-906
ISSN:1303-5991
Container-title:Communications Faculty Of Science University of Ankara Series A1Mathematics and Statistics
language:en
Short-container-title:Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat.

Author:

ŞENYURT Süleyman¹^ORCID,CANLI Davut²^ORCID,ÇAN Elif²^ORCID,GÜR MAZLUM Sümeyye³^ORCID

Affiliation:

1. ORDU ÜNİVERSİTESİ

2. ORDU UNIVERSITY

3. GUMUSHANE UNIVERSITY

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.

Publisher

Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics

Subject

General Medicine

Reference36 articles.

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