Integrable hierarchies and the modular class

2006/07/30 by Pantelis A. Damianou, Rui Loja Fernandes, Damianou, Pantelis A. +1
Computer Science · Mathematics · Physics and Astronomy · #37J35 #53D17 #Advanced Topics in Algebra #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #Homotopy and Cohomology in Algebraic Topology #Logic, Reasoning, and Knowledge #Mathematical Physics (math-ph) #math-ph #math.DG #math.MP #msc:37J35 #msc:53D17

paper · pdf · doi:10.48550/arxiv.math/0607784

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

openalex publication_date 2006/07/30 · arxiv created 2006/10/11 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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