Hamiltonian Evolutions of Curves in Classical Affine Geometries
نویسنده
چکیده
In this paper we study geometric Poisson brackets and we show that, if M = (G n IRn)/G endowed with an affine geometry (in the Klein sense), and if G is a classical Lie group, then the geometric Poisson bracket for parametrized curves is a trivial extension of the one for unparametrized curves, except for the case G = GL(n, IR). This trivial extension does not exist in other nonaffine cases (projective, conformal, etc).
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