
Journal of Lie Theory 13 (2003), No. 1, 213245 Copyright Heldermann Verlag 2003 Relative and Absolute Differential Invariants for Conformal Curves Gloria Mari Beffa Dept. of Mathematics, University of Wisconsin, Madison, WI 53706, U.S.A. We classify all vector relative differential invariants with Jacobian weight for the conformal action of O(n+1, 1) on parametrized curves in 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 by A. Fialkow ["The conformal theory of curves", Transactions of the AMS 51 (1942) 435456]. As a corollary, we obtain the most general formula for evolutions of curves in R^{n } invariant under the conformal action of the group. [ Fulltextpdf (267 KB)] for subscribers only. 