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<p>In this paper, we investigate the parallel curves, involutes and pre-evolutes of an equi-centro-affine framed curve in equi-centro-affine plane. Meanwhile, we give the existence and uniqueness theorems of equi-centro-affine framed curves. Moreover, based on the equi-centro-affine framed curve, we analyse the singular properties of the parallel curves, involutes, and pre-evolutes of an equi-centro-affine framed curve. Finally, several examples are presented to illustrate our conclusions.</p>

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Curves in Equi-centro-affine Plane

  • 期刊论文

  • 发表日期：

    2025年7月31日

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  • Yi Li,
  • Pengcheng Li,
  • Donghe Pei

摘要

In this paper, we investigate the parallel curves, involutes and pre-evolutes of an equi-centro-affine framed curve in equi-centro-affine plane. Meanwhile, we give the existence and uniqueness theorems of equi-centro-affine framed curves. Moreover, based on the equi-centro-affine framed curve, we analyse the singular properties of the parallel curves, involutes, and pre-evolutes of an equi-centro-affine framed curve. Finally, several examples are presented to illustrate our conclusions.