Translation surfaces of coordinate finite type

Hassan Al-Zoubi; Stylianos Stamatakis; Waseem Al-Mashaleh; Mohammed Awadallah

Translation surfaces of coordinate finite type

Hassan Al-Zoubi
, Stylianos Stamatakis
, Waseem Al-Mashaleh
, Mohammed Awadallah

Al-Zaytoonah University of Jordan
Aristotle University of Thessaloniki
Al-Aqsa University

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

15 Scopus citations

Abstract

We consider translation surfaces in the 3-dimensional Euclidean space which are. of coordinate finite type with respect to the third fundamental form III, i.e. their position vector x satisfies the relation Δ^III x = Λx, where Λ is a square matrix of order 3. We show that Sherk's minimal surface is the only translation surface satisfying Δ^III x = Λ x.

Original language	English
Pages (from-to)	227-241
Number of pages	15
Journal	Indian Journal of Mathematics
Volume	59
Issue number	2
State	Published - Aug 2017
Externally published	Yes

Keywords

Beltrami operator
Surfaces in Euclidean space
Surfaces of coordinate finite type

Cite this

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title = "Translation surfaces of coordinate finite type",

abstract = "We consider translation surfaces in the 3-dimensional Euclidean space which are. of coordinate finite type with respect to the third fundamental form III, i.e. their position vector x satisfies the relation ΔIII x = Λx, where Λ is a square matrix of order 3. We show that Sherk's minimal surface is the only translation surface satisfying ΔIII x = Λ x.",

keywords = "Beltrami operator, Surfaces in Euclidean space, Surfaces of coordinate finite type",

author = "Hassan Al-Zoubi and Stylianos Stamatakis and Waseem Al-Mashaleh and Mohammed Awadallah",

note = "Publisher Copyright: {\textcopyright} 2017 Allahabad Mathematical Society.",

year = "2017",

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language = "English",

volume = "59",

pages = "227--241",

journal = "Indian Journal of Mathematics",

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TY - JOUR

T1 - Translation surfaces of coordinate finite type

AU - Al-Zoubi, Hassan

AU - Stamatakis, Stylianos

AU - Al-Mashaleh, Waseem

AU - Awadallah, Mohammed

PY - 2017/8

Y1 - 2017/8

N2 - We consider translation surfaces in the 3-dimensional Euclidean space which are. of coordinate finite type with respect to the third fundamental form III, i.e. their position vector x satisfies the relation ΔIII x = Λx, where Λ is a square matrix of order 3. We show that Sherk's minimal surface is the only translation surface satisfying ΔIII x = Λ x.

AB - We consider translation surfaces in the 3-dimensional Euclidean space which are. of coordinate finite type with respect to the third fundamental form III, i.e. their position vector x satisfies the relation ΔIII x = Λx, where Λ is a square matrix of order 3. We show that Sherk's minimal surface is the only translation surface satisfying ΔIII x = Λ x.

KW - Beltrami operator

KW - Surfaces in Euclidean space

KW - Surfaces of coordinate finite type

UR - https://www.scopus.com/pages/publications/85031093759

M3 - Article

AN - SCOPUS:85031093759

SN - 0019-5324

VL - 59

SP - 227

EP - 241

JO - Indian Journal of Mathematics

JF - Indian Journal of Mathematics

IS - 2

ER -

Translation surfaces of coordinate finite type

Abstract

Keywords

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