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General-Affine Invariants of Plane Curves and Space Curves
| 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: https://doi.org/10.21136/CMJ.2019.0165-18 |
| Type: | article (author version) |
| URI: | http://hdl.handle.net/2115/80516 |
| 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)
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Submitter: 小林 真平
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