a1 Department of Mathematical Sciences, The University of Liverpool, Mathematics and Oceanography Building, Peach Street, Liverpool L69 7ZL, UK (email@example.com)
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)