Journal of Lie Theory Vol. 13, No. 1, pp. 231245 (2003) 

Relative and Absolute Differential Invariants for Conformal CurvesGloria Marí BeffaGloria Marí BeffaMathematics Department U. of Wisconsin Madison WI 53706 USA maribeff@math.wisc.edu Abstract: In this paper we classify all vector relative differential invariants with Jacobian weight for the conformal action of O$(n+1,1)$ on parametrized curves in ${\Bbb R}^{n}$. We then write a generating set of independent conformal differential invariants, for both parametrized and unparametrized curves, as simple combinations of the relative invariants. We also find an invariant frame for unparametrized curves via a GramSchmidt procedure. The invariants of unparametrized curves correspond to the ones found in Fialkow, A., {\it The Conformal Theory of Curves}, ``Transactions of the AMS'' {\bf 51} (1942), 43556. As a corollary, we obtain the most general formula for evolutions of curves in ${\Bbb R}^{n}$ invariant under the conformal action of the group. Full text of the article:
Electronic fulltext finalized on: 22 Nov 2002. This page was last modified: 3 Jan 2003.
© 2002 Heldermann Verlag
