May 7, 2024Open Access

Ruled Ricci surfaces and curves of constant torsion

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Abstract

We show that all non-developable ruled surfaces endowed with Ricci metrics in the three-dimensional Euclidean space may be constructed using curves of constant torsion and its binormal. This allows us to give characterizations of the helicoid as the only surface of this kind that admits a parametrization with plane line of striction, and as the only with constant mean curvature.

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Carvalho et al. (Tue,) studied this question.

synapsesocial.com/papers/68e6b4c2b6db64358763597e https://doi.org/https://doi.org/10.48550/arxiv.2405.04255

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