Geodesic
Transvection and Differential Invariants of Parametrized Curves
Journal of Lie theory, Tome 18 (2008) no. 1, pp. 93-123
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We describe an sl2 representation in the space of differential invariants of parametrized curves in homogeneous spaces. The representation is described by three operators, one of them being the total derivative D. We use this representation to find a basis for the space of differential invariants of curves in a complement of the image of D, and so generated by transvection. These are natural representatives of first cohomology classes in the invariant bicomplex. We describe algorithms to find these basis and study most well-known geometries.
Classification : 13A50, 53A55
Mots-clés : Transvectant, differential invariants, curves, affine manifold, symmetric manifold 
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     author = {G. Mar{\'\i} Beffa and J. A. Sanders},
     title = {Transvection and {Differential} {Invariants} of {Parametrized} {Curves}},
     journal = {Journal of Lie theory},
     pages = {93--123},
     year = {2008},
     volume = {18},
     number = {1},
     url = {http://geodesic.mathdoc.fr/item/JLT_2008_18_1_JLT_2008_18_1_a6/}
}
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G. Marí Beffa; J. A. Sanders. Transvection and Differential Invariants of Parametrized Curves. Journal of Lie theory, Tome 18 (2008) no. 1, pp. 93-123. http://geodesic.mathdoc.fr/item/JLT_2008_18_1_JLT_2008_18_1_a6/