Surfaces of coordinate finite II-type

Mutaz Al-Sabbagh

doi:10.3934/math.2025285

Surfaces of coordinate finite II-type

Mutaz Al-Sabbagh^*

^*Corresponding author for this work

Basic Engineering Sciences

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

Abstract

We study the class of surfaces of revolution in the 3-dimensional Euclidean space E³ with nonvanishing Gauss curvature whose position vector x satisfies the condition ∆^II x = Ax, where A is a square matrix of order 3 and ∆^II denotes the Laplace operator of the second fundamental form II of the surface. We show that a surface of revolution satisfying the preceding relation is a catenoid or part of a sphere.

Original language	English
Pages (from-to)	6258-6269
Number of pages	12
Journal	AIMS Mathematics
Volume	10
Issue number	3
DOIs	https://doi.org/10.3934/math.2025285
State	Published - 2025

Keywords

Beltrami operator
surfaces in E
surfaces of coordinate finite type
surfaces of revolution

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10.3934/math.2025285

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title = "Surfaces of coordinate finite II-type",

abstract = "We study the class of surfaces of revolution in the 3-dimensional Euclidean space E3 with nonvanishing Gauss curvature whose position vector x satisfies the condition ∆II x = Ax, where A is a square matrix of order 3 and ∆II denotes the Laplace operator of the second fundamental form II of the surface. We show that a surface of revolution satisfying the preceding relation is a catenoid or part of a sphere.",

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N2 - We study the class of surfaces of revolution in the 3-dimensional Euclidean space E3 with nonvanishing Gauss curvature whose position vector x satisfies the condition ∆II x = Ax, where A is a square matrix of order 3 and ∆II denotes the Laplace operator of the second fundamental form II of the surface. We show that a surface of revolution satisfying the preceding relation is a catenoid or part of a sphere.

AB - We study the class of surfaces of revolution in the 3-dimensional Euclidean space E3 with nonvanishing Gauss curvature whose position vector x satisfies the condition ∆II x = Ax, where A is a square matrix of order 3 and ∆II denotes the Laplace operator of the second fundamental form II of the surface. We show that a surface of revolution satisfying the preceding relation is a catenoid or part of a sphere.

KW - Beltrami operator

KW - surfaces in E

KW - surfaces of coordinate finite type

KW - surfaces of revolution

UR - https://www.scopus.com/pages/publications/105001443252

U2 - 10.3934/math.2025285

DO - 10.3934/math.2025285

M3 - Article

AN - SCOPUS:105001443252

SN - 2473-6988

VL - 10

SP - 6258

EP - 6269

JO - AIMS Mathematics

JF - AIMS Mathematics

IS - 3

ER -

Surfaces of coordinate finite II-type

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