Generalized Weierstrass-Enneper representation for minimal surfaces in $ \mathbb{R}^4 $

Magdalena Toda; Erhan Güler; Magdalena Toda; Erhan Güler

doi:10.3934/math.2025997

AIMS Mathematics

2025, Volume 10, Issue 9: 22406-22420. doi: 10.3934/math.2025997

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Research article

Generalized Weierstrass-Enneper representation for minimal surfaces in $ \mathbb{R}^4 $

Magdalena Toda ,
Erhan Güler ^,

Department of Mathematics and Statistics, College of Arts and Sciences, Texas Tech University, Lubbock, TX 79409, USA

Received: 13 August 2025 Revised: 18 September 2025 Accepted: 23 September 2025 Published: 28 September 2025
MSC : 53A10, 53C42

In this study, we present a generalized Weierstrass-Enneper representation for minimal surfaces in four-dimensional Euclidean space. We derive both parametric (explicit) and algebraic (implicit) representations of several example minimal surfaces, examine their differential-geometric properties, and visualize them through orthogonal projections from $ \mathbb{R}^4 $ into $ \mathbb{R}^3 $.
- $ \mathbb{R}^4 $,
- minimal surface,
- generalized Weierstrass-Enneper representation,
- Gauss map,
- holomorphic curves
Citation: Magdalena Toda, Erhan Güler. Generalized Weierstrass-Enneper representation for minimal surfaces in $ \mathbb{R}^4 $[J]. AIMS Mathematics, 2025, 10(9): 22406-22420. doi: 10.3934/math.2025997

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Abstract

In this study, we present a generalized Weierstrass-Enneper representation for minimal surfaces in four-dimensional Euclidean space. We derive both parametric (explicit) and algebraic (implicit) representations of several example minimal surfaces, examine their differential-geometric properties, and visualize them through orthogonal projections from $ \mathbb{R}^4 $ into $ \mathbb{R}^3 $.

References

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