The Chen type of Hasimoto surfaces in the Euclidean 3-space

Hassan Al-Zoubi; Bendehiba Senoussi; Mutaz Al-Sabbagh; Mehmet Ozdemir

doi:10.3934/math.2023819

The Chen type of Hasimoto surfaces in the Euclidean 3-space

Hassan Al-Zoubi^*
, Bendehiba Senoussi
, Mutaz Al-Sabbagh
, Mehmet Ozdemir

^*Corresponding author for this work

Basic Engineering Sciences

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

5 Scopus citations

Abstract

A surface M² with position vector r = r(s, t) is called a Hasimoto surface if the relation r_t = r_s ∧ r_ss holds. In this paper, we first define the Beltrami-Laplace operator according to the three fundamental forms of the surface, then we classify the J-harmonic Hasimoto surfaces and their Gauss map in E³, for J = II and III.

Original language	English
Pages (from-to)	16062-16072
Number of pages	11
Journal	AIMS Mathematics
Volume	8
Issue number	7
DOIs	https://doi.org/10.3934/math.2023819
State	Published - 2023

Keywords

Beltrami-Laplace operator
Euclidean space
Gauss map
Hasimoto surface
surfaces of finite type

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10.3934/math.2023819

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title = "The Chen type of Hasimoto surfaces in the Euclidean 3-space",

abstract = "A surface M2 with position vector r = r(s, t) is called a Hasimoto surface if the relation rt = rs ∧ rss holds. In this paper, we first define the Beltrami-Laplace operator according to the three fundamental forms of the surface, then we classify the J-harmonic Hasimoto surfaces and their Gauss map in E3, for J = II and III.",

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author = "Hassan Al-Zoubi and Bendehiba Senoussi and Mutaz Al-Sabbagh and Mehmet Ozdemir",

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T1 - The Chen type of Hasimoto surfaces in the Euclidean 3-space

AU - Al-Zoubi, Hassan

AU - Senoussi, Bendehiba

AU - Al-Sabbagh, Mutaz

AU - Ozdemir, Mehmet

PY - 2023

Y1 - 2023

N2 - A surface M2 with position vector r = r(s, t) is called a Hasimoto surface if the relation rt = rs ∧ rss holds. In this paper, we first define the Beltrami-Laplace operator according to the three fundamental forms of the surface, then we classify the J-harmonic Hasimoto surfaces and their Gauss map in E3, for J = II and III.

AB - A surface M2 with position vector r = r(s, t) is called a Hasimoto surface if the relation rt = rs ∧ rss holds. In this paper, we first define the Beltrami-Laplace operator according to the three fundamental forms of the surface, then we classify the J-harmonic Hasimoto surfaces and their Gauss map in E3, for J = II and III.

KW - Beltrami-Laplace operator

KW - Euclidean space

KW - Gauss map

KW - Hasimoto surface

KW - surfaces of finite type

UR - https://www.scopus.com/pages/publications/85159068334

U2 - 10.3934/math.2023819

DO - 10.3934/math.2023819

M3 - Article

AN - SCOPUS:85159068334

SN - 2473-6988

VL - 8

SP - 16062

EP - 16072

JO - AIMS Mathematics

JF - AIMS Mathematics

IS - 7

ER -

The Chen type of Hasimoto surfaces in the Euclidean 3-space

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Keywords

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