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

Alexandre Paiva Barreto; Fernando Gasparotto

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arXiv · 2303.03623

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

Alexandre Paiva Barreto·Fernando Gasparotto

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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 $S$.

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BibTeX RIS

Alexandre Paiva Barreto, Fernando Gasparotto. 2023-03-07. Polynomial Weingarten Tubular Surfaces in Euclidean, Hyperbolic and Lorentzian 3-spaces. https://arxiv.org/abs/2303.03623

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