Geodesic
Relative and Absolute Differential Invariants for Conformal Curves
Journal of Lie theory, Tome 13 (2003) no. 1, pp. 213-245 Cet article a éte moissonné depuis la source Heldermann Verlag

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We classify all vector relative differential invariants with Jacobian weight for the conformal action of  O(n+1, 1) on parametrized curves in  Rn.  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 Gram-Schmidt 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) 435--456].  As a corollary, we obtain the most general formula for evolutions of curves in  Rn  invariant under the conformal action of the group. 
@article{JLT_2003_13_1_JLT_2003_13_1_a12,
     author = {G. Mari Beffa },
     title = {Relative and {Absolute} {Differential} {Invariants} for {Conformal} {Curves}},
     journal = {Journal of Lie theory},
     pages = {213--245},
     year = {2003},
     volume = {13},
     number = {1},
     url = {http://geodesic.mathdoc.fr/item/JLT_2003_13_1_JLT_2003_13_1_a12/}
}
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G. Mari Beffa . Relative and Absolute Differential Invariants for Conformal Curves. Journal of Lie theory, Tome 13 (2003) no. 1, pp. 213-245. http://geodesic.mathdoc.fr/item/JLT_2003_13_1_JLT_2003_13_1_a12/