Generic affine differential geometry of curves in Rn

Author:

Davis Declan

Abstract

This paper considers curves in Rn. It defines affine arc length and affine curvatures. The family of affine distance functions is generalized, along with the family of affine height functions. A new basis is constructed that makes the conditions for Ak singularity types easier to calculate, and applications are given to geometrical problems.

Publisher

Cambridge University Press (CUP)

Subject

General Mathematics

Cited by 12 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. Lancret-type theorems in equiaffine space;Journal of Geometry;2024-06-05

2. Fractional Curvatures of Equiaffine Curves in Three-Dimensional Affine Space;Journal of New Theory;2024-03-29

3. On Curves with Affine-Congruent Arcs in an $ n $-Dimensional Affine Space;Siberian Mathematical Journal;2022-01

4. Applications of fractional calculus in equiaffine geometry: plane curves with fractional order;Mathematical Methods in the Applied Sciences;2021-07-18

5. On the affine measurement of arcs of a moment curve;Sibirskie Elektronnye Matematicheskie Izvestiya;2019-09-27

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