Poisson Geometry of Differential Invariants of Curves in Some Nonsemisimple Homogenous Spaces
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چکیده
In this paper we describe a family of compatible Poisson structures defined on the space of coframes (or differential invariants) of curves in flat homogeneous spaces of the form M ∼= (G n IRn)/G where G ⊂ GL(n, IR) is semisimple. This includes Euclidean, affine, special affine, Lorentz, and symplectic geometries. We also give conditions on geometric evolutions of curves in the manifold M so that the induced evolution on their differential invariants is Hamiltonian with respect to our main Hamiltonian bracket.
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تاریخ انتشار 2014