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<p>The aim of this paper is to derive the biharmonic spacelike curves and slant curves in the roto-translation group equipped with the first Lorentz metric. First, the Frenet–Serret equations and the concept of biharmonic mappings are introduced. Second, these properties are utilized to uncover the relationship between curvature and torsion for two types of non-geodesic Frenet special curves: biharmonic spacelike curves and slant curves. Finally, an example is provided to illustrate and characterize these two types of special curves.</p>

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Biharmonic curve in roto-translation group

  • 期刊论文

  • 发表日期：

    2025年11月14日

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  • Han Zhang,
  • Jiajing Miao,
  • Jianyun Guan,
  • Haiming Liu

摘要

The aim of this paper is to derive the biharmonic spacelike curves and slant curves in the roto-translation group equipped with the first Lorentz metric. First, the Frenet–Serret equations and the concept of biharmonic mappings are introduced. Second, these properties are utilized to uncover the relationship between curvature and torsion for two types of non-geodesic Frenet special curves: biharmonic spacelike curves and slant curves. Finally, an example is provided to illustrate and characterize these two types of special curves.