GEOMETRY OF CURVES PASSING THROUGH THE WHITNEY UMBRELLA

Kyushu Journal of Mathematics 2026 Open access

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Authors: Hiroyuki Hayashi
DOI: 10.2206/kyushujm.80.281
Cited by: 0

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.

Fields of Study & Subjects

Advanced Numerical Analysis Techniques Mathematics and Applications Computational Geometry and Mesh Generation

Publication details

Journal / source
Kyushu Journal of Mathematics
Volume
80
Issue
2
Pages
281–299
Publication date
1 January 2026
Language
EN