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

Gloria Marí Beffa[1]

  • [1] University of Wisconsin Mathematics department Madison, Wisconsin 53706 (USA)

Annales de l’institut Fourier (2011)

  • Volume: 61, Issue: 6, page 2405-2434
  • ISSN: 0373-0956

Abstract

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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 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.

How to cite

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Marí Beffa, Gloria. "Moving frames, Geometric Poisson brackets and the KdV-Schwarzian evolution of pure spinors." Annales de l’institut Fourier 61.6 (2011): 2405-2434. <http://eudml.org/doc/219747>.

@article{MaríBeffa2011,
abstract = {In this paper we describe a non-local moving frame along a curve of pure spinors in $\mathrm\{O\}(2m,2m)/P$, 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.},
affiliation = {University of Wisconsin Mathematics department Madison, Wisconsin 53706 (USA)},
author = {Marí Beffa, Gloria},
journal = {Annales de l’institut Fourier},
keywords = {Moving frame; spinor evolutions; geometric Poisson brackets; KdV equations; differential invariants; Miura transformation; non-commutative modified KdV system; moving frame},
language = {eng},
number = {6},
pages = {2405-2434},
publisher = {Association des Annales de l’institut Fourier},
title = {Moving frames, Geometric Poisson brackets and the KdV-Schwarzian evolution of pure spinors},
url = {http://eudml.org/doc/219747},
volume = {61},
year = {2011},
}

TY - JOUR
AU - Marí Beffa, Gloria
TI - Moving frames, Geometric Poisson brackets and the KdV-Schwarzian evolution of pure spinors
JO - Annales de l’institut Fourier
PY - 2011
PB - Association des Annales de l’institut Fourier
VL - 61
IS - 6
SP - 2405
EP - 2434
AB - In this paper we describe a non-local moving frame along a curve of pure spinors in $\mathrm{O}(2m,2m)/P$, 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.
LA - eng
KW - Moving frame; spinor evolutions; geometric Poisson brackets; KdV equations; differential invariants; Miura transformation; non-commutative modified KdV system; moving frame
UR - http://eudml.org/doc/219747
ER -

References

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