English

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