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arXiv · 2108.02769

Poisson quasi-Nijenhuis deformations of the canonical PN structure

Gregorio Falqui·Igor Mencattini·Marco Pedroni
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Abstract

We present a result which allows us to deform a Poisson-Nijenhuis manifold into a Poisson quasi-Nijenhuis manifold by means of a closed 2-form. Under an additional assumption, the deformed structure is also Poisson-Nijenhuis. We apply this result to show that the canonical Poisson-Nijenhuis structure on R^2n gives rise to both the Poisson-Nijenhuis structure of the open (or non periodic) n-particle Toda lattice, introduced by Das and Okubo [6], and the Poisson quasi-Nijenhuis structure of the closed (or periodic) n-particle Toda lattice, described in our recent work [7].

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Gregorio Falqui, Igor Mencattini, Marco Pedroni. 2021-08-05. Poisson quasi-Nijenhuis deformations of the canonical PN structure. https://arxiv.org/abs/2108.02769

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