This article is cited in 35 papers

On the 60th birthday of professor V.V. Kozlov

Poisson structures for geometric curve flows in semi-simple homogeneous spaces

G. Marí Beffa^a, P. J. Olver<sup>b

a</sup> Department of Mathematics, University of Wisconsin, Madison, Wisconsin 53706, USA
^b School of Mathematics, University of Minnesota, Minneapolis, Minnesota 55455, USA

Abstract: We apply the equivariant method of moving frames to investigate the existence of Poisson structures for geometric curve flows in semi-simple homogeneous spaces. We derive explicit compatibility conditions that ensure that a geometric flow induces a Hamiltonian evolution of the associated differential invariants. Our results are illustrated by several examples of geometric interest.

Keywords: moving frame, Poisson structure, homogeneous space, invariant curve flow, differential invariant, invariant variational bicomplex.

MSC: 22F05, 35A30, 35Q53, 53A55, 58A20, 53D17

Received: 12.10.2009
Accepted: 13.03.2010

Language: English

DOI: 10.1134/S156035471004009X

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