In this paper we describe the close relationship between invariant evolutions of projective curves and the Hamiltonian evolutions of Adler, Gel'fand and Dikii. We also show how KdV evolutions are related as well to invariant evolutions of projective surfaces.
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...
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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