English

Harmonic Enneper Immersion in $\mathbb{R}^3$

Differential Geometry 2026-03-23 v1

Abstract

We present a method for constructing harmonic immersions in R3\mathbb{R}^3, known as the Enneper-type representation. We also prove that any harmonic immersion in R3\mathbb{R}^3 can be obtained using this approach. Furthermore, we determine the number of non-planar rotational harmonic immersions in R3\mathbb{R}^3 that connect two coaxial circles in parallel planes, where both circles have the same radius r>0r > 0 and are separated by a distance l>0l > 0.

Cite

@article{arxiv.2603.19783,
  title  = {Harmonic Enneper Immersion in $\mathbb{R}^3$},
  author = {Priyank Vasu},
  journal= {arXiv preprint arXiv:2603.19783},
  year   = {2026}
}
R2 v1 2026-07-01T11:29:32.539Z