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Moving frames, Geometric Poisson brackets and the KdV-Schwarzian evolution of pure spinors

Gloria Marí Beffa (2011)

Annales de l’institut Fourier

In this paper we describe a non-local moving frame along a curve of pure spinors in O ( 2 m , 2 m ) / P , 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...

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