Journal of Lie Theory

no. 1
Relative and Absolute Differential Invariants for Conformal Curves
Journal of Lie Theory, Volume 13 (2003) no. 1, pp. 213-245
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.
DOI: 10.5802/jolt.299
Classification: 53A55
Keywords: conformal curves, invariants, Schwarzian derivative 
@article{JOLT_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},
     doi = {10.5802/jolt.299},
     zbl = {1028.53015},
     url = {https://jolt.centre-mersenne.org/articles/10.5802/jolt.299/}
}
TY  - JOUR
AU  - G. 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  - https://jolt.centre-mersenne.org/articles/10.5802/jolt.299/
DO  - 10.5802/jolt.299
ID  - JOLT_2003_13_1_a12
ER  - 
%0 Journal Article
%A G. 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 https://jolt.centre-mersenne.org/articles/10.5802/jolt.299/
%R 10.5802/jolt.299
%F JOLT_2003_13_1_a12
G. Mari Beffa. Relative and Absolute Differential Invariants for Conformal Curves. Journal of Lie Theory, Volume 13 (2003) no. 1, pp. 213-245. doi: 10.5802/jolt.299

Cited by Sources: