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Research Article | Open Access

Surface family pair with Bertrand pair as mutual geodesic curves in Euclidean 3-space E 3

Areej A. Almoneef1( ), Rashad A. Abdel-Baky2
Department of Mathematical Sciences, College of Science, Princess Nourah bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi Arabia
Department of Mathematics, Faculty of Science, University of Assiut 71516, Egypt
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Abstract

The main interest of this work is to construct surface family pair with the symmetry of Bertrand pair in Euclidean 3-space E 3 . Then, by employing the Serret-Frenet frame, we conclude the sufficient and necessary conditions of surface family pair interpolating Bertrand pair as mutual geodesic curves. Moreover, the conclusion to ruled surface family pair is also obtained. Meanwhile, this work is demonstrated through several examples.

Keywords

geodesic curveBertrand materuled surface
CLC number: 53A04, 53A05, 53A17

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AIMS Mathematics
Volume 8 Issue 9,
September 2023
Pages 20546-20560
DOI: 10.3934/math.20231047

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Cite this article:
Almoneef AA, Abdel-Baky RA. Surface family pair with Bertrand pair as mutual geodesic curves in Euclidean 3-space E 3 . AIMS Mathematics, 2023, 8(9): 20546-20560. https://doi.org/10.3934/math.20231047

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Received: 14 May 2023
Revised: 17 June 2023
Accepted: 20 June 2023
Published: 15 September 2023
©2023 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)