Scholarlink

<p>In this paper, we define primitive surfaces of curves in the Euclidean 3-space. The correlations between primitive surfaces and pedals, pedal surfaces in the Euclidean 3-space are established. By using the singularity theory, we give the classification of singularities of primitive surfaces. We find these singularities are closely related to the contact between the spatial curves and specific spheres. Moreover, we study primitive surfaces from the viewpoint of spherical Legendrian dualities. At last, several examples are provided to demonstrate our results.</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

Primitive surfaces of curves in the Euclidean 3-space

  • 期刊论文

  • 发表日期：

    2025年8月18日

查看全文
  • Yongqiao Wang,
  • Chao Jia,
  • Yuxin Liu,
  • Yuan Chang

摘要

In this paper, we define primitive surfaces of curves in the Euclidean 3-space. The correlations between primitive surfaces and pedals, pedal surfaces in the Euclidean 3-space are established. By using the singularity theory, we give the classification of singularities of primitive surfaces. We find these singularities are closely related to the contact between the spatial curves and specific spheres. Moreover, we study primitive surfaces from the viewpoint of spherical Legendrian dualities. At last, several examples are provided to demonstrate our results.