The higher-order Henneberg-type minimal surfaces family in $\mathbb{R}^4$
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866915661787168768 |
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| author | Güler, Erhan Toda, Magdalena |
| author_facet | Güler, Erhan Toda, Magdalena |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_07852 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The higher-order Henneberg-type minimal surfaces family in $\mathbb{R}^4$ Güler, Erhan Toda, Magdalena Differential Geometry 53A10, 53C42 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. |
| title | The higher-order Henneberg-type minimal surfaces family in $\mathbb{R}^4$ |
| topic | Differential Geometry 53A10, 53C42 |
| url | https://arxiv.org/abs/2512.07852 |