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Research Article | Open Access

Surfaces of coordinate finite I I-type

Department of Basic Engineering Sciences, Imam Abdulrahman bin Faisal University, Dammam 31441, Saudi Arabia
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Abstract

We study the class of surfaces of revolution in the 3-dimensional Euclidean space E 3 with nonvanishing Gauss curvature whose position vector x satisfies the condition Δ I I x = A x, where A is a square matrix of order 3 and Δ I I denotes the Laplace operator of the second fundamental form I I of the surface. We show that a surface of revolution satisfying the preceding relation is a catenoid or part of a sphere.

Keywords

surfaces in E3surfaces of revolutionsurfaces of coordinate finite typeBeltrami operator
CLC number: 53A05, 53A45

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AIMS Mathematics
Volume 10 Issue 3,
March 2025
Pages 6258-6269
DOI: 10.3934/math.2025285

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Al-Sabbagh M. Surfaces of coordinate finite I I-type. AIMS Mathematics, 2025, 10(3): 6258-6269. https://doi.org/10.3934/math.2025285

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Received: 23 January 2025
Revised: 05 March 2025
Accepted: 12 March 2025
Published: 15 March 2025
©2025 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)