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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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Mathyze Publishers
2024-12-01
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| 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. |
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| ISSN: | 2832-4293 |