Scholarlink

<p>We prove that general helices in Euclidean space for Killing vector fields associated to rotations are helices, that is, curves with constant curvature and constant torsion. In hyperbolic space <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\({\mathbb {H}}^3\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mrow> <mi mathvariant="double-struck">H</mi> </mrow> <mn>3</mn> </msup> </math></EquationSource> </InlineEquation>, we obtain the parametrizations of helices for all types of Killing vector fields. It is proved that these helices are geodesics in suitable surfaces of <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\({\mathbb {H}}^3\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mrow> <mi mathvariant="double-struck">H</mi> </mrow> <mn>3</mn> </msup> </math></EquationSource> </InlineEquation>.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

A note on helices in the Euclidean space and in the hyperbolic space

  • 期刊论文

  • 出版模式：

    开放获取

  • 发表日期：

    2025年8月22日

查看全文
  • Rafael López

摘要

We prove that general helices in Euclidean space for Killing vector fields associated to rotations are helices, that is, curves with constant curvature and constant torsion. In hyperbolic space \({\mathbb {H}}^3\) H 3 , we obtain the parametrizations of helices for all types of Killing vector fields. It is proved that these helices are geodesics in suitable surfaces of \({\mathbb {H}}^3\) H 3 .