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Research Article | Open Access

Quadric surfaces of finite Chen Ⅱ-type

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

In this paper we studied quadric surfaces in the Euclidean 3-space that were of finite type with respect to the second fundamental form Ⅱ. The main result presented in this article was that spheres were the only quadric surfaces of finite type. This indicated a specific and notable classification within the broader category of quadric surfaces based on their finite type characteristics in relation to the second fundamental form.

Keywords

surfaces in 3-spacefinite Chen-type surfacessecond Beltrami operatorquadric surfaces
CLC number: 53A05, 53A45

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AIMS Mathematics
Volume 9 Issue 12,
December 2024
Pages 34435-34446
DOI: 10.3934/math.20241640

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Al-Sabbagh M. Quadric surfaces of finite Chen Ⅱ-type. AIMS Mathematics, 2024, 9(12): 34435-34446. https://doi.org/10.3934/math.20241640

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Received: 11 October 2024
Revised: 28 November 2024
Accepted: 29 November 2024
Published: 15 December 2024
©2024 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)