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Research Article | Open Access

The Chen type of Hasimoto surfaces in the Euclidean 3-space

Hassan Al-Zoubi1( ), Bendehiba Senoussi2, Mutaz Al-Sabbagh3, Mehmet Ozdemir3
Department of Mathematics, Al-Zaytoonah University of Jordan, P.O. Box 130, Amman, Jordan 11733
Department of Mathematics, Ecole Normale Superieure, 45 rue d'Ulm, 75230, Mostaganem, Algeria
Department of Basic Engineering Sciences, Imam Abdulrahman bin Faisal University, Dammam 31441, Saudi Arabia
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Abstract

A surface M 2 with position vector r = r ( s , t ) is called a Hasimoto surface if the relation r t = r s ∧ r s s holds. In this paper, we first define the Beltrami-Laplace operator according to the three fundamental forms of the surface, then we classify the J-harmonic Hasimoto surfaces and their Gauss map in E 3 , for J = I I and I I I.

Keywords

Hasimoto surfaceGauss mapEuclidean spaceBeltrami-Laplace operatorsurfaces of finite type
CLC number: 14J25, 53Z05

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AIMS Mathematics
Volume 8 Issue 7,
July 2023
Pages 16062-16072
DOI: 10.3934/math.2023819

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Cite this article:
Al-Zoubi H, Senoussi B, Al-Sabbagh M, et al. The Chen type of Hasimoto surfaces in the Euclidean 3-space. AIMS Mathematics, 2023, 8(7): 16062-16072. https://doi.org/10.3934/math.2023819

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Received: 25 February 2023
Revised: 23 April 2023
Accepted: 24 April 2023
Published: 15 July 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)