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- Publisher
- Springer Journals
- Copyright
- Copyright © 2009 by Springer Science+Business Media B.V.
- Subject
- Mathematics; Mechanics; Statistical Physics, Dynamical Systems and Complexity; Theoretical, Mathematical and Computational Physics; Computer Science, general; Mathematics, general
- ISSN
- 0167-8019
- eISSN
- 1572-9036
- DOI
- 10.1007/s10440-009-9444-2
- Publisher site
- See Article on Publisher Site
Abstract
We study pairs of structures, such as the Poisson-Nijenhuis structures, on the tangent bundle of a manifold or, more generally, on a Lie algebroid or a Courant algebroid. These composite structures are defined by two of the following, a closed 2-form, a Poisson bivector or a Nijenhuis tensor, with suitable compatibility assumptions. We establish the relationships between PN-, P Ω- and Ω N-structures. We then show that the non-degenerate Monge-Ampère structures on 2-dimensional manifolds satisfying an integrability condition provide numerous examples of such structures, while in the case of 3-dimensional manifolds, such Monge-Ampère operators give rise to generalized complex structures or generalized product structures on the cotangent bundle of the manifold.
Journal
Acta Applicandae Mathematicae – Springer Journals
Published: Feb 3, 2009