Proceedings of the Royal Society of Edinburgh: Section A Mathematics

Research Article

Generic affine differential geometry of curves in Rn

Declan Davisa1

a1 Department of Mathematical Sciences, The University of Liverpool, Mathematics and Oceanography Building, Peach Street, Liverpool L69 7ZL, UK (


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.

(Received April 08 2005)

(Accepted November 30 2005)