Geometric realizations of bi-Hamiltonian completely integrable systems.
The theory of differential invariants and KDV hamiltonian evolutions
Moving frames, Geometric Poisson brackets and the KdV-Schwarzian evolution of pure spinors
In this paper we describe a non-local moving frame along a curve of pure spinors in , and its associated basis of differential invariants. We show that the space of differential invariants of Schwarzian-type define a Poisson submanifold of the spinor Geometric Poisson brackets. The resulting restriction is given by a decoupled system of KdV Poisson structures. We define a generalization of the Schwarzian-KdV evolution for pure spinor curves and we prove that it induces a decoupled system of KdV...
Projective-type differential invariants and geometric curve evolutions of KdV-type in flat homogeneous manifolds
In this paper we describe moving frames and differential invariants for curves in two different -graded parabolic manifolds , and , and we define differential invariants of projective-type. We then show that, in the first case, there are geometric flows in inducing equations of KdV-type in the projective-type differential invariants when proper initial conditions are chosen. We also show that geometric Poisson brackets in the space of differential invariants of curves in can be reduced...
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