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<p>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.</p>

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Ruled Ricci surfaces and curves of constant torsion

  • 期刊论文

  • 发表日期：

    2025年3月7日

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  • Alcides de Carvalho,
  • Iury Domingos,
  • Roney Santos

摘要

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.