Normal form of $D_4^-$-singularities of fronts and its applications

Kentaro Saji

Normal form of $D_4^-$-singularities of fronts and its applications

Differential Geometry 2026-06-28 v1

Authors: Kentaro Saji

Abstract

We construct a form of the $D_4^-$ -singularity of fronts in $\R^3$ which uses coordinate transformation on the source and isometry on the target. As an application, we compute differential geometric invariants near the $D_4^-$ -singularity, and give a Gauss-Bonnet type theorem for one-parameter generic fronts.

Keywords

front singularities normal form coordinate transformation isometry differential geometric invariants Gauss-Bonnet theorem

Cite

@article{arxiv.2606.29491,
  title  = {Normal form of $D_4^-$-singularities of fronts and its applications},
  author = {Kentaro Saji},
  journal= {arXiv preprint arXiv:2606.29491},
  year   = {2026}
}

Comments

20 pages, 4 figures