The Algebraic Surfaces of the Enneper Family of Maximal Surfaces in Three Dimensional Minkowski Space

Güler, Erhan

doi:10.3390/axioms11010004

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2022

2023

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Cited by 3 publications

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References 12 publications

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“…Lie [10] studied algebraic minimal surfaces and gave a table for these kinds of surfaces. See also [6,[16][17][18][19][20][21][22][23][24] for details.…”

Section: Introductionmentioning

confidence: 99%

(ζ−m, ζm)-Type Algebraic Minimal Surfaces in Three-Dimensional Euclidean Space

Güler

Kı̇şı̇

2022

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We introduce the real minimal surfaces family by using the Weierstrass data (ζ−m,ζm) for ζ∈C, m∈Z≥2, then compute the irreducible algebraic surfaces of the surfaces family in three-dimensional Euclidean space E3. In addition, we propose that family has a degree number (resp., class number) 2m(m+1) in the cartesian coordinates x,y,z (resp., in the inhomogeneous tangential coordinates a,b,c).

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“…Lie [10] studied algebraic minimal surfaces and gave a table for these kinds of surfaces. See also [6,[16][17][18][19][20][21][22][23][24] for details.…”

Section: Introductionmentioning

confidence: 99%

(ζ−m, ζm)-Type Algebraic Minimal Surfaces in Three-Dimensional Euclidean Space

Güler

Kı̇şı̇

2022

Axioms

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On the Gaussian curvature of timelike surfaces in Lorentz-Minkowski 3-space

Gür Mazlum

2023

Filomat

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The algebraic surfaces of the minimal-maximal surfaces

Güler,

Kişi

2023

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Considering soft computing, the Weierstrass data (??1/2, ?1/2) gives two different minimal surface equations and figures. By using hard computing, we give the family of minimal and spacelike maximal surfaces S(m,n) for natural numbers m and n in Euclidean and Minkowski 3-spaces E3, E2,1, respectively. We obtain the classes and degrees of surfaces S(m,n). Considering the integral free form of Weierstrass, we define some algebraic functions for S(m,n). Indicating several maximal surfaces of value (m, n) are algebraic, we recall Weierstrass-type representations for maximal surfaces in E2,1, and give explicit parametrizations for spacelike maximal surfaces of value (m, n). Finally, we compute the implicit equations, degree, and class of the spacelike maximal surfaces S(0,1), S(1,1) and S(2,1) in terms of their cartesian or inhomogeneous tangential coordinates in E2,1.

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The Algebraic Surfaces of the Enneper Family of Maximal Surfaces in Three Dimensional Minkowski Space

Cited by 3 publications

References 12 publications

(ζ−m, ζm)-Type Algebraic Minimal Surfaces in Three-Dimensional Euclidean Space

(ζ−m, ζm)-Type Algebraic Minimal Surfaces in Three-Dimensional Euclidean Space

On the Gaussian curvature of timelike surfaces in Lorentz-Minkowski 3-space

The algebraic surfaces of the minimal-maximal surfaces

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