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arXiv · 1105.4858

Reduction of Poisson-Nijenhuis Lie algebroids to symplectic-Nijenhuis Lie algebroids with nondegenerate Nijenhuis tensor

Antonio De Nicola·Juan Carlos Marrero·Edith Padron
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Abstract

We show how to reduce, under certain regularities conditions, a Poisson-Nijenhuis Lie algebroid to a symplectic-Nijenhuis Lie algebroid with nondegenerate Nijenhuis tensor. We generalize the work done by Magri and Morosi for the reduction of Poisson-Nijenhuis manifolds. The choice of the more general framework of Lie algebroids is motivated by the geometrical study of some reduced bi-Hamiltonian systems. An explicit example of reduction of a Poisson-Nijenhuis Lie algebroid is also provided.

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Antonio De Nicola, Juan Carlos Marrero, Edith Padron. 2011-05-24. Reduction of Poisson-Nijenhuis Lie algebroids to symplectic-Nijenhuis Lie algebroids with nondegenerate Nijenhuis tensor. https://doi.org/10.1088/1751-8113/44/42/425206

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