English

Classifications of cusps appearing on plane curves

Differential Geometry 2024-02-20 v1

Abstract

In this paper, we deal with plane curves with cusps. It is well known that there are various types of cusps. Among them, we investigate criteria for (n,n+1)(n, n+1) cusps with respect to several differential conditions and relations between these singularities and evolutes of fronts. We give complete classifications with respect to (4,5)(4, 5)-cusps.

Keywords

Cite

@article{arxiv.2402.12166,
  title  = {Classifications of cusps appearing on plane curves},
  author = {Yoshiki Matsushita},
  journal= {arXiv preprint arXiv:2402.12166},
  year   = {2024}
}

Comments

16 pages, 3 figures

R2 v1 2026-06-28T14:53:11.244Z