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General-affine invariants of plane curves and space curves

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Publication:6314774

DOI10.21136/CMJ.2019.0165-18arXiv1902.10926MaRDI QIDQ6314774

Author name not available (Why is that?)

Publication date: 28 February 2019

Abstract: We present a fundamental theory of curves in the affine plane and the affine space, equipped with the general-affine groups and , 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.





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