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Research Article | Open Access

Generalized Weierstrass-Enneper representation for minimal surfaces in R 4

Magdalena Toda, Erhan Güler( )
Department of Mathematics and Statistics, College of Arts and Sciences, Texas Tech University, Lubbock, TX 79409, USA
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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 R 4 into R 3 .

Keywords

R4minimal surfacegeneralized Weierstrass-Enneper representationGauss mapholomorphic curves
CLC number: 53A10, 53C42

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AIMS Mathematics
Volume 10 Issue 9,
September 2025
Pages 22406-22420
DOI: 10.3934/math.2025997

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Cite this article:
Toda M, Güler E. Generalized Weierstrass-Enneper representation for minimal surfaces in R 4 . AIMS Mathematics, 2025, 10(9): 22406-22420. https://doi.org/10.3934/math.2025997

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Received: 13 August 2025
Revised: 18 September 2025
Accepted: 23 September 2025
Published: 28 September 2025
©2025 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)