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<p>As a generalization of lightcone framed curves in Lorentz-Minkowski 3-space, we put forward the definition of lightcone framed curves in de Sitter 2-space as the first step to study the mixed type curves with singularities in non-flat space. We also show the Uniqueness and Existence of this kind of curves. By using the lightcone frame, we define de Sitter evolutes and hyperbolic evolutes of lightcone framed curves that possess not only lightlike points but also singular points in de Sitter 2-space. We show relationships between the points of evolutes and those of lightcone framed curves. Moreover, we prove that the evolutes are not the lightcone framed curves in de Sitter 2-space, but the lightcone framed curves in Lorentz-Minkowski 3-space. We also take into account the singularities of the lightcone framed curves and those of their evolutes.</p>

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Evolutes of lightcone framed curves in de Sitter 2-space

  • 期刊论文

  • 发表日期：

    2026年1月6日

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  • Chang Xu,
  • Liang Chen

摘要

As a generalization of lightcone framed curves in Lorentz-Minkowski 3-space, we put forward the definition of lightcone framed curves in de Sitter 2-space as the first step to study the mixed type curves with singularities in non-flat space. We also show the Uniqueness and Existence of this kind of curves. By using the lightcone frame, we define de Sitter evolutes and hyperbolic evolutes of lightcone framed curves that possess not only lightlike points but also singular points in de Sitter 2-space. We show relationships between the points of evolutes and those of lightcone framed curves. Moreover, we prove that the evolutes are not the lightcone framed curves in de Sitter 2-space, but the lightcone framed curves in Lorentz-Minkowski 3-space. We also take into account the singularities of the lightcone framed curves and those of their evolutes.