Geometry of curves passing through Whitney umbrella
Differential Geometry
2025-11-11 v2 Geometric Topology
Abstract
We study geometry of curves passing through a Whitney umbrella by using a Darboux frame along it. We define three invariants by using Frenet-Serre type formula relating to the geodesic curvature, the normal curvature, and the geodesic torsion. We investigate the degrees of divergence and the top-terms of these invariants and their geometric meanings. We also consider a developable surface along the curve.
Cite
@article{arxiv.2410.00459,
title = {Geometry of curves passing through Whitney umbrella},
author = {Hiroyuki Hayashi},
journal= {arXiv preprint arXiv:2410.00459},
year = {2025}
}