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<p>In this paper we use the notion of helix associated to a <i>F</i>-constant vector field, which has cylindrical and slant helices as particular examples, to find its natural equation. In the case of normal helices, we prove that they are characterized by being the pseudo-geodesics of helix surfaces.</p>

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The natural equations of three-dimensional helices

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年1月21日

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  • Pascual Lucas,
  • José Antonio Ortega-Yagües

摘要

In this paper we use the notion of helix associated to a F-constant vector field, which has cylindrical and slant helices as particular examples, to find its natural equation. In the case of normal helices, we prove that they are characterized by being the pseudo-geodesics of helix surfaces.