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Generic affine differential geometry of curves in Rn

Published online by Cambridge University Press:  12 July 2007

Declan Davis
Declan Davis
Affiliation:
Department of Mathematical Sciences, The University of Liverpool, Mathematics and Oceanography Building, Peach Street, Liverpool L69 7ZL, UK ([email protected])
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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.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 136 , Issue 6 , December 2006 , pp. 1195 - 1205
Copyright
Copyright © Royal Society of Edinburgh 2006

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