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Singularities of tangent surfaces to directed curves

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Title: Singularities of tangent surfaces to directed curves
Authors: Ishikawa, G. Browse this author →KAKEN DB
Yamashita, T. Browse this author
Keywords: Affine connection
Open swallowtail
Issue Date: 1-Feb-2018
Publisher: Elsevier
Journal Title: Topology and its applications
Volume: 234
Start Page: 198
End Page: 208
Publisher DOI: 10.1016/j.topol.2017.11.018
Abstract: 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. (C) 2017 Elsevier B.V. All rights reserved.
Rights: ©2017 This manuscript version is made available under the CC-BY-NC-ND 4.0 license
Type: article (author version)
Appears in Collections:理学院・理学研究院 (Graduate School of Science / Faculty of Science) > 雑誌発表論文等 (Peer-reviewed Journal Articles, etc)

Submitter: 石川 剛郎

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