Translation surfaces generating with some partner curve-Reference-Cited by-同舟云学术

Translation surfaces generating with some partner curve

Published:2023-10-23 Issue:1 Volume:73 Page:165-177
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:

HAS Aykut¹^ORCID,YILMAZ Beyhan¹^ORCID

Affiliation:

1. KAHRAMANMARAS SUTCU IMAM UNIVERSITY

Abstract

In this article, generating curves of translation surfaces are paired with some special curve pairs. With the results obtained from these pairings, the developable and minimal translation surfaces are characterized. In addition, the surface curvatures of the translation surface are obtained. For a better understanding of the results, examples are given and their drawings are made with the help of Mathematica.

Publisher

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

Reference26 articles.

1. Bertrand, J. M., Memoire sur la theorie des courbes a double courbure, Comptes Rendus, 15 (1850), 332–350.

2. Mannheim, A., De l’emploi de la courbe representative de la surface des normales principales d’une courbe gauche pour la d´emonstration de proprietes relatives a cette courbure, Comptes Rendus des Seances de l’Acad´emie des Sciences, 86 (1878), 1254-1256.

3. Do Cormo, M. P., Differential Geometry of Curves and Surfaces, Prentice-Hall, New Jersey, 1976.

4. Eren, K., Ayvacı, K. H., Şenyurt, S., On ruled surfaces constructed by the evolution of a polynomial space curve, Journal of Science and Arts, 23(1) (2023), 77-90. https://doi.org/10.46939/J.Sci.Arts-23.1-a06

5. Has, A., Yılmaz, B., Yaylı, Y., Constant angle ruled surfaces in E31 , Fundamental Journal of Mathematics and Applications, 6 (2023), 78-88. https://doi.org/10.33401/fujma.1218966