Quadric surfaces of finite Chen II-type

Mutaz Al-Sabbagh

doi:10.3934/math.20241640

Quadric surfaces of finite Chen II-type

Mutaz Al-Sabbagh^*

^*Corresponding author for this work

Basic Engineering Sciences

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Pages (from-to)	34435-34446
Number of pages	12
Journal	AIMS Mathematics
Volume	9
Issue number	12
DOIs	https://doi.org/10.3934/math.20241640
State	Published - 2024

Keywords

finite Chen-type surfaces
quadric surfaces
second Beltrami operator
surfaces in 3-space

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10.3934/math.20241640

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title = "Quadric surfaces of finite Chen II-type",

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 = "finite Chen-type surfaces, quadric surfaces, second Beltrami operator, surfaces in 3-space",

author = "Mutaz Al-Sabbagh",

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year = "2024",

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AU - Al-Sabbagh, Mutaz

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N2 - 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.

AB - 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.

KW - finite Chen-type surfaces

KW - quadric surfaces

KW - second Beltrami operator

KW - surfaces in 3-space

UR - https://www.scopus.com/pages/publications/85212082025

U2 - 10.3934/math.20241640

DO - 10.3934/math.20241640

M3 - Article

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VL - 9

SP - 34435

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JO - AIMS Mathematics

JF - AIMS Mathematics

IS - 12

ER -

Quadric surfaces of finite Chen II-type

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