General-Affine Invariants of Plane Curves and Space Curves

Kobayashi, Shimpei; Sasaki, Takeshi

Czechoslovak Mathematical Journal, 2020, 70(1), 67-104

Permalink : https://hdl.handle.net/2115/80516

このアイテムのアクセス数:402件（2026-10-11 18:48 集計）

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Czech. Math. J.70-1_67-104	pdf	488 KB	388

アクセス権	open access
URI	https://hdl.handle.net/2115/80516
タイトル	General-Affine Invariants of Plane Curves and Space Curves
著者	e-Rad_Researcher 40408654 著者名 Kobayashi, Shimpei
著者	著者名 Sasaki, Takeshi
言語	英語
キーワード	plane curve
	space curve
	general-affine group
	general-affine curvature
	variational problem
発行日	2020-03
出版者	Springer
収録物名	Czechoslovak Mathematical Journal
巻(号)	70(1)
ページ	67-104
抄録	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.
資源タイプ	学術雑誌論文
出版タイプ	Submitted Manuscript Under Review
権利情報	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
PISSN	0011-4642
関連情報 (isVersionOf)	出版社版DOI https://doi.org/10.21136/CMJ.2019.0165-18