arXiv Open Access 2016

Singularities of tangent surfaces to directed curves

G. Ishikawa T. Yamashita

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Abstrak

A directed curve is a possibly singular curve with well-defined tangent lines along the curve. Then the tangent surface to a directed curve is naturally defined as the ruled surface by tangent geodesics to the curve, whenever any affine connection is endowed with the ambient space. In this paper the local diffeomorphism classification is completed for generic directed curves. Then it turns out that the swallowtails and open swallowtails appear generically for the classification on singularities of tangent surfaces.

Topik & Kata Kunci

math.DG

Penulis (2)

G. Ishikawa

T. Yamashita

Format Sitasi

APA MLA BibTeX

Ishikawa, G., Yamashita, T. (2016). Singularities of tangent surfaces to directed curves. https://arxiv.org/abs/1607.08702

Akses Cepat

Lihat di Sumber

Informasi Jurnal

Tahun Terbit: 2016
Bahasa: en
Sumber Database: arXiv
Akses: Open Access ✓