J. C. Alvarez-paiva and C. E. Durán, Geometric invariants of fanning curves, Advances in Applied Mathematics, vol.42, issue.3, pp.290-312, 2009.
DOI : 10.1016/j.aam.2006.07.008

T. Barbot, V. Charette, T. Drumm, W. M. Goldman, and K. Melnick, A primer on the (2 + 1) Einstein universe. In Recent developments in pseudo- Riemannian geometry, ESI Lect, Math. Phys, pp.179-229, 2008.

F. Boulier and E. Hubert, diffalg: description, help pages and examples of use. Symbolic Computation Group, 1998.

R. Capovilla, J. Guven, and E. Rojas, Null Frenet-Serret dynamics, General Relativity and Gravitation, vol.543, issue.4, pp.689-698, 2006.
DOI : 10.1007/s10714-006-0258-5

E. Cartan, Sur leprobì eme général de la déformation, C.R. Congrés de Strasbourg, pp.397-406, 1920.

S. S. Chern and H. C. Wang, Differential geometry in symplectic space, I. Sci. Rep. Nat. Tsing Hua Univ, vol.4, pp.453-477, 1947.

V. Deconchy, Hypersurfaces in symplectic affine geometry, Differential Geometry and its Applications, vol.17, issue.1, pp.1-13, 2002.
DOI : 10.1016/S0926-2245(01)00067-5

M. Fels and P. J. Olver, Moving coframes. II. Regularization and theoretical foundations, Acta Applicandae Mathematicae, vol.55, issue.2, pp.127-208, 1999.
DOI : 10.1023/A:1006195823000

A. Feoli, V. V. Nesterenko, and G. Scarpetta, Functionals linear in curvature and statistics of helical proteins, Nuclear Physics B, vol.705, issue.3, pp.577-592, 2005.
DOI : 10.1016/j.nuclphysb.2004.10.062

P. Griffiths, On Cartan's method of Lie groups and moving frames as applied to uniqueness and existence questions in differential geometry. Duke Math, 11] P. A. Griffiths. Exterior differential systems and the calculus of variations, pp.775-814, 1974.

V. Guillemin and S. Sternberg, Variations on a theme by Kepler, 1990.
DOI : 10.1090/coll/042

E. Hubert, diffalg: extension to non commuting derivations

E. Hubert, Differential algebra for derivations with nontrivial commutation rules, Journal of Pure and Applied Algebra, vol.200, issue.1-2, pp.163-190, 2005.
DOI : 10.1016/j.jpaa.2004.12.034
URL : https://hal.archives-ouvertes.fr/inria-00071606

E. Hubert, The maple package aida -Algebraic Invariants and their Differential Algebras. INRIA, 2007.

E. Hubert, Differential invariants of a Lie group action: Syzygies on a generating set, Journal of Symbolic Computation, vol.44, issue.4, pp.382-416, 2009.
DOI : 10.1016/j.jsc.2008.08.003
URL : https://hal.archives-ouvertes.fr/inria-00178189

E. Hubert, Algebraic and Differential Invariants, Foundations of computational mathematics, 2011.
DOI : 10.1017/CBO9781139095402.009
URL : https://hal.archives-ouvertes.fr/hal-00763310

E. Hubert, Generation properties of Maurer-Cartan invariants, 2012.
URL : https://hal.archives-ouvertes.fr/inria-00194528

E. Hubert and I. A. Kogan, Smooth and Algebraic Invariants of a Group Action: Local and Global Constructions, Foundations of Computational Mathematics, vol.7, issue.4, 2007.
DOI : 10.1007/s10208-006-0219-0
URL : https://hal.archives-ouvertes.fr/inria-00198857

E. Hubert and P. J. Olver, Differential invariants of conformal and projective surfaces. Symmetry Integrability and Geometry: Methods and Applications, 2007.
URL : https://hal.archives-ouvertes.fr/inria-00198876

J. Inoguchi and S. Lee, Null curves in Minkowski 3-space, Int. Electron. J. Geom, vol.1, issue.2, pp.40-83, 2008.

T. A. Ivey and J. M. Landsberg, Cartan for beginners: differential geometry via moving frames and exterior differential systems, Graduate Studies in Mathematics, vol.61, 2003.

G. R. Jensen, Deformation of submanifolds of homogeneous spaces, Journal of Differential Geometry, vol.16, issue.2, pp.213-246, 1981.
DOI : 10.4310/jdg/1214436100

N. Kamran, P. Olver, and K. Tenenblat, LOCAL SYMPLECTIC INVARIANTS FOR CURVES, Communications in Contemporary Mathematics, vol.11, issue.02, pp.165-183, 2009.
DOI : 10.1142/S0219199709003326

I. A. Kogan and P. J. Olver, Invariant Euler-Lagrange equations and the invariant variational bicomplex, Acta Applicandae Mathematicae, vol.76, issue.2, pp.137-193, 2003.
DOI : 10.1023/A:1022993616247

Y. Kuznetsov and M. Plyushchay, (2+1)???dimensional models of relativistic particles with curvature and torsion, Journal of Mathematical Physics, vol.35, issue.6, pp.2772-2778, 1994.
DOI : 10.1063/1.530485

E. L. Mansfield, A Practical Guide to the Invariant Calculus, 2010.
DOI : 10.1017/CBO9780511844621

G. and M. Beffa, On completely integrable geometric evolutions of curves of Lagrangian planes, Proceedings of the Royal Society of Edinburgh: Section A Mathematics, vol.137, issue.01, pp.111-131, 2007.
DOI : 10.1017/S0308210505000600

G. and M. Beffa, Hamiltonian evolution of curves in classical affine geometries, Physica D. Nonlinear Phenomena, vol.238, issue.1, pp.100-115, 2009.

B. Mckay, Lagrangian submanifolds in affine symplectic geometry, Differential Geometry and its Applications, vol.24, issue.6, pp.670-689, 2006.
DOI : 10.1016/j.difgeo.2006.04.003

E. Musso and J. D. Grant, Coisotropic variational problems, Journal of Geometry and Physics, vol.50, issue.1-4, pp.303-338, 2004.
DOI : 10.1016/j.geomphys.2003.10.005

E. Musso and L. Nicolodi, Closed trajectories of a particle model on null curves in anti-de Sitter 3-space, Classical and Quantum Gravity, vol.24, issue.22, pp.5401-5411, 2007.
DOI : 10.1088/0264-9381/24/22/005

E. Musso and L. Nicolodi, Symplectic applicability of Lagrangian surfaces. SIGMA Symmetry Integrability Geom, Methods Appl, vol.5, issue.18, p.67, 2009.

E. Musso and L. Nicolodi, Hamiltonian flows on null curves, Nonlinearity, vol.23, issue.9, pp.2117-2129, 2010.
DOI : 10.1088/0951-7715/23/9/005

L. Musso and E. Nicolodi, Reduction for Constrained Variational Problems on 3-Dimensional Null Curves, SIAM Journal on Control and Optimization, vol.47, issue.3, pp.1399-1414, 2008.
DOI : 10.1137/070686470

A. Nersessian, R. Manvelyan, and H. J. Müller-kirsten, Particle with torsion on 3d null-curves, Constrained dynamics and quantum gravity, pp.381-384, 1999.
DOI : 10.1016/S0920-5632(00)00807-0

V. V. Nesterenko, Curvature and torsion of the world curve in the action of the relativistic particle, Journal of Mathematical Physics, vol.32, issue.12, pp.3315-3320, 1991.
DOI : 10.1063/1.529494

V. V. Nesterenko, A. Feoli, and G. Scarpetta, Dynamics of relativistic particles with Lagrangians dependent on acceleration, Journal of Mathematical Physics, vol.36, issue.10, pp.5552-5564, 1995.
DOI : 10.1063/1.531332

V. V. Nesterenko, A. Feoli, and G. Scarpetta, Complete integrability for Lagrangians dependent on acceleration in a spacetime of constant curvature, Classical and Quantum Gravity, vol.13, issue.5, pp.1201-1211, 1996.
DOI : 10.1088/0264-9381/13/5/030

P. J. Olver, Applications of Lie Groups to Differential Equations. Number 107 in Graduate texts in Mathematics, 1986.

P. J. Olver, Equivalence, Invariants and Symmetry, 1995.
DOI : 10.1017/CBO9780511609565

P. J. Olver, Generating differential invariants, Journal of Mathematical Analysis and Applications, vol.333, issue.1, pp.450-471, 2007.
DOI : 10.1016/j.jmaa.2006.12.029

R. W. Sharpe, Differential geometry, volume 166 of Graduate Texts in Mathematics, 1997.

F. Valiquette, Geometric affine symplectic curve flows in <mml:math altimg="si1.gif" overflow="scroll" xmlns:xocs="http://www.elsevier.com/xml/xocs/dtd" xmlns:xs="http://www.w3.org/2001/XMLSchema" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns="http://www.elsevier.com/xml/ja/dtd" xmlns:ja="http://www.elsevier.com/xml/ja/dtd" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:tb="http://www.elsevier.com/xml/common/table/dtd" xmlns:sb="http://www.elsevier.com/xml/common/struct-bib/dtd" xmlns:ce="http://www.elsevier.com/xml/common/dtd" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:cals="http://www.elsevier.com/xml/common/cals/dtd"><mml:msup><mml:mrow><mml:mi mathvariant="double-struck">R</mml:mi></mml:mrow><mml:mrow><mml:mn>4</mml:mn></mml:mrow></mml:msup></mml:math>, Differential Geometry and its Applications, vol.30, issue.6, pp.631-641, 2012.
DOI : 10.1016/j.difgeo.2012.09.003