Differential Geometry and Integrability of the Hamiltonian System of a Closed Vortex Filament
نویسنده
چکیده
The system of a closed vortex filament is an integrable Hamiltonian one, namely, a Hamiltonian system with an infinite sequense of constants of motion in involution. An algebraic framework is given for the aim of describing differential geometry of this system. A geometrical structure related to the integrability of this system is revealed. It is not a bi-Hamiltonian structure but similar one. As a related topic, a remark on the inspection of J. Langer and R. Perline, J. Nonlinear Sci. 1, 71 (1991), is given. Mathematics Subject Classification (1991). 58F07, 76C05.
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