  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.
