Rotational Surfaces in Terms of Coordinate Finite Chen II-Type

In this study, we first establish several formulae according to the first and second Beltrami operators. We discuss the class of surfaces of revolution in the 3-dimensional Euclidean space E3 without parabolic points, in which the position vector X satisfies ∆IIX = DX, with ∆II is the Laplace operat...

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Bibliographic Details
Main Authors: Hamza Alzaareer, Hassan Al-Zoubi
Format: Article
Language:English
Published: Mathyze Publishers 2024-12-01
Series:Pan-American Journal of Mathematics
Online Access:https://mathyze.com/index.php/pajm/article/view/241
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Summary:In this study, we first establish several formulae according to the first and second Beltrami operators. We discuss the class of surfaces of revolution in the 3-dimensional Euclidean space E3 without parabolic points, in which the position vector X satisfies ∆IIX = DX, with ∆II is the Laplace operator of the metric II of the surface and D is a square matrix of order 3. We prove that surfaces satisfying the preceding relation are either part of a sphere or catenoid.
ISSN:2832-4293