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Singularities of tangent surfaces to generic space curves

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Title: Singularities of tangent surfaces to generic space curves
Authors: Ishikawa, G. Browse this author →KAKEN DB
Yamashita, T. Browse this author
Issue Date: Apr-2017
Publisher: Springer
Journal Title: Journal of Geometry
Volume: 108
Issue: 1
Start Page: 301
End Page: 318
Publisher DOI: 10.1007/s00022-016-0341-3
Abstract: 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.
Rights: The final publication is available at link.springer.com
Type: article (author version)
URI: http://hdl.handle.net/2115/68649
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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