The higher-order Henneberg-type minimal surfaces family in $\mathbb{R}^4$

Erhan Güler; Magdalena Toda

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arXiv · 2512.07852

The higher-order Henneberg-type minimal surfaces family in $\mathbb{R}^4$

Erhan Güler·Magdalena Toda

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Abstract

We consider a higher-order Henneberg-type minimal surfaces family using the generalized Weierstrass--Enneper representation in four-dimensional space $\mathbb{R}^4$. We derive explicit parametric equations for the surface and determine its differential geometric characteristics, including the normal vector fields $\mathbf{n}_1$ and $\mathbf{n}_2$, as well as the Gauss curvature. Furthermore, by projecting these parametric forms from four to three dimensions, we generate visualizations that reveal the geometric structure of the Henneberg-type minimal surface. In addition, we examine the integral-free form and derive the corresponding algebraic function for this family of surfaces.

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BibTeX RIS

Erhan Güler, Magdalena Toda. 2025-11-26. The higher-order Henneberg-type minimal surfaces family in $\mathbb{R}^4$. https://arxiv.org/abs/2512.07852

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