Moving Frames, Geometric Poisson Brackets and the Kdv-schwarzian Evolution of Pure Spinors
نویسنده
چکیده
In this paper we describe a non-local moving frame along a curve of pure spinors in O(2m, 2m)/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 equations on the invariants of projective type, when restricted to a certain level set. We also describe its associated Miura transformation and non-commutative modified KdV system.
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