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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Poisson geometry of differential invariants of curves in some nonsemisimple homogeneous spaces
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by G. Marí Beffa PDF
Proc. Amer. Math. Soc. 134 (2006), 779-791 Request permission

Abstract:

In this paper we describe a family of compatible Poisson structures defined on the space of coframes (or differential invariants) of curves in flat homogeneous spaces of the form $\mathcal {M} \cong (G\ltimes \mathbb {R}^n)/G$ where $G\subset {\mathrm {GL}}(n,\mathbb {R})$ is semisimple. This includes Euclidean, affine, special affine, Lorentz, and symplectic geometries. We also give conditions on geometric evolutions of curves in the manifold $\mathcal {M}$ so that the induced evolution on their differential invariants is Hamiltonian with respect to our main Hamiltonian bracket.
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Additional Information
  • G. Marí Beffa
  • Affiliation: Department of Mathematics, University of Wisconsin, Madison, Wisconsin 53706
  • Email: maribeff@math.wisc.edu
  • Received by editor(s): August 20, 2004
  • Received by editor(s) in revised form: October 15, 2004
  • Published electronically: July 19, 2005
  • Communicated by: Jozef Dodziuk
  • © Copyright 2005 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Proc. Amer. Math. Soc. 134 (2006), 779-791
  • MSC (2000): Primary 37K25; Secondary 37K05, 37K10, 53A55
  • DOI: https://doi.org/10.1090/S0002-9939-05-07998-0
  • MathSciNet review: 2180896