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

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.

35 pages, final version to appear in J. Phys. A: Math. Theor

References in corpus (4)

• Lagrangian submanifolds and dynamics on Lie algebroids
• Classical field theory on Lie algebroids: Variational aspects
• Modular classes of Poisson-Nijenhuis Lie algebroids
• A class of Poisson-Nijenhuis structures on a tangent bundle