Poisson geometry of differential invariants of curves in some nonsemisimple homogeneous spaces

Author:
G. Marí Beffa

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

Published electronically:
July 19, 2005

MathSciNet review:
2180896

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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 where is semisimple. This includes Euclidean, affine, special affine, Lorentz, and symplectic geometries. We also give conditions on geometric evolutions of curves in the manifold 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

DOI:
https://doi.org/10.1090/S0002-9939-05-07998-0

Keywords:
Invariant evolutions of curves,
homogeneous spaces,
infinite dimensional Poisson geometry,
differential invariants,
completely integrable PDEs

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

Article copyright:
© Copyright 2005
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication.