Integrable hierarchies and the modular class
Differential Geometry
2007-05-23 v2 Mathematical Physics
math.MP
Abstract
We observe that the modular class of a Poisson-Nijhenhuis manifold has a canonical representative and that, under a cohomological assumption, this vector field is bi-hamiltonian. In many examples the associated hierarchy of flows reproduces classical integrable hierarchies.
Keywords
Cite
@article{arxiv.math/0607784,
title = {Integrable hierarchies and the modular class},
author = {Pantelis A. Damianou and Rui Loja Fernandes},
journal= {arXiv preprint arXiv:math/0607784},
year = {2007}
}
Comments
26 pages, 27 references. One major change: the assumption on non-degeneracy of the Poisson tensor on a PN manifold was dropped. Several minor changes and 2 new references included