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General-Affine Invariants of Plane Curves and Space Curves

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Title: General-Affine Invariants of Plane Curves and Space Curves
Authors: Kobayashi, Shimpei Browse this author →KAKEN DB
Sasaki, Takeshi Browse this author
Keywords: plane curve
space curve
general-affine group
general-affine curvature
variational problem
Issue Date: Mar-2020
Publisher: Springer
Journal Title: Czechoslovak Mathematical Journal
Volume: 70
Issue: 1
Start Page: 67
End Page: 104
Publisher DOI: 10.21136/CMJ.2019.0165-18
Abstract: We present a fundamental theory of curves in the affine plane and the affine space, equipped with the general-affine groups GA(2) = GL(2, Double-struck capital R); Double-struck capital R-2 and GA(3) = GL(3, Double-struck capital R); Double-struck capital R-3, respectively. We define general-affine length parameter and curvatures and show how such invariants determine the curve up to general-affine motions. We then study the extremal problem of the general-affine length functional and derive a variational formula. We give several examples of curves and also discuss some relations with equiaffine treatment and projective treatment of curves.
Rights: This is a pre-print of an article published in Czechoslovak Mathematical Journal. The final authenticated version is available online at:
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: 小林 真平

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