Polynomial Weingarten Tubular Surfaces in Euclidean, Hyperbolic and Lorentzian 3-spaces

Alexandre Paiva Barreto; Fernando Gasparotto

Polynomial Weingarten Tubular Surfaces in Euclidean, Hyperbolic and Lorentzian 3-spaces

Differential Geometry 2023-03-08 v1

Authors: Alexandre Paiva Barreto , Fernando Gasparotto

Abstract

In this article we fully classify regular tubular surfaces in Euclidean, Lorentzian and hyperbolic 3-spaces whose Gaussian and mean curvatures $K$ and $H$ verify a polynomial relation. More precisely, we determine the set $S(Q)$ of all regular tubular surfaces whose curvatures verify a given polynomial relation $Q(K,H)=0$ , and the set $Q(S)$ of all polynomial relations vanished by the curvatures of a given tubular surface $S$ .

Keywords

tubular surfaces gaussian curvature mean curvature polynomial relation euclidean 3-space hyperbolic 3-space lorentzian 3-space

Cite

@article{arxiv.2303.03623,
  title  = {Polynomial Weingarten Tubular Surfaces in Euclidean, Hyperbolic and Lorentzian 3-spaces},
  author = {Alexandre Paiva Barreto and Fernando Gasparotto},
  journal= {arXiv preprint arXiv:2303.03623},
  year   = {2023}
}

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