Harmonic Enneper Immersion in $\mathbb{R}^3$
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arXiv
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866910061216923648 |
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| author | Vasu, Priyank |
| author_facet | Vasu, Priyank |
| contents | We present a method for constructing harmonic immersions in $\mathbb{R}^3$, known as the Enneper-type representation. We also prove that any harmonic immersion in $\mathbb{R}^3$ can be obtained using this approach. Furthermore, we determine the number of non-planar rotational harmonic immersions in $\mathbb{R}^3$ that connect two coaxial circles in parallel planes, where both circles have the same radius $r > 0$ and are separated by a distance $l > 0$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_19783 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Harmonic Enneper Immersion in $\mathbb{R}^3$ Vasu, Priyank Differential Geometry 53C43, 30C62, 53A10 We present a method for constructing harmonic immersions in $\mathbb{R}^3$, known as the Enneper-type representation. We also prove that any harmonic immersion in $\mathbb{R}^3$ can be obtained using this approach. Furthermore, we determine the number of non-planar rotational harmonic immersions in $\mathbb{R}^3$ that connect two coaxial circles in parallel planes, where both circles have the same radius $r > 0$ and are separated by a distance $l > 0$. |
| title | Harmonic Enneper Immersion in $\mathbb{R}^3$ |
| topic | Differential Geometry 53C43, 30C62, 53A10 |
| url | https://arxiv.org/abs/2603.19783 |