1Dept. of Mathematics, University of Wisconsin, Madison, WI 53706, U.S.A. 2We classify all vector relative differential invariants with Jacobian weight for the conformal action of O(n+1, 1) on parametrized curves in R 3. 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 R 4invariant under the conformal action of the group. 5[
Journal of Lie Theory, Tome 13 (2003) no. 1, pp. 213-245
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Gloria 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/JOLT_2003_13_1_a12/
@article{JOLT_2003_13_1_a12,
author = {Gloria 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/JOLT_2003_13_1_a12/}
}
TY - JOUR
AU - Gloria Mari Beffa
TI - Relative and Absolute Differential Invariants for Conformal Curves
JO - Journal of Lie Theory
PY - 2003
SP - 213
EP - 245
VL - 13
IS - 1
UR - http://geodesic.mathdoc.fr/item/JOLT_2003_13_1_a12/
ID - JOLT_2003_13_1_a12
ER -
%0 Journal Article
%A Gloria Mari Beffa
%T Relative and Absolute Differential Invariants for Conformal Curves
%J Journal of Lie Theory
%D 2003
%P 213-245
%V 13
%N 1
%U http://geodesic.mathdoc.fr/item/JOLT_2003_13_1_a12/
%F JOLT_2003_13_1_a12
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.
