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arXiv · 2410.00459

Geometry of curves passing through Whitney umbrella

Hiroyuki Hayashi
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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.

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Hiroyuki Hayashi. 2024-10-01. Geometry of curves passing through Whitney umbrella. https://arxiv.org/abs/2410.00459

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