open access

https://hdl.handle.net/2115/68649

Singularities of tangent surfaces to generic space curves

英語

2017-04

Springer

Journal of Geometry

108(1)

301-318

We give the complete solution to the local diffeomorphism classification problem of generic singularities which appear in tangent surfaces, in as wider situations as possible. We interpret tangent geodesics as tangent lines whenever a (semi-) Riemannian metric, or, more generally, an affine connection is given in an ambient space of arbitrary dimension. Then, given an immersed curve, we define the tangent surface as the ruled surface by tangent geodesics to the curve. We apply the characterization of frontal singularities found by Kokubu, Rossman, Saji, Umehara, Yamada, and Fujimori, Saji, Umehara, Yamada, and found by the first author related to the procedure of openings of singularities.

学術雑誌論文

Accepted Manuscript

The final publication is available at link.springer.com

0047-2468