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 R2n gives rise to both the Poisson-Nijenhuis structure of the open (or non periodic) n-particle Toda lattice, introduced by Das and Okubo [7], and the Poisson quasi-Nijenhuis structure of the closed (or periodic) n-particle Toda lattice, described in our recent work [8].

Falqui, G., Mencattini, I., Pedroni, M. (2023). Poisson quasi-Nijenhuis deformations of the canonical PN structure. JOURNAL OF GEOMETRY AND PHYSICS, 186(April 2023), 1-10 [10.1016/j.geomphys.2023.104773].

Poisson quasi-Nijenhuis deformations of the canonical PN structure

Falqui G.;
2023

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 R2n gives rise to both the Poisson-Nijenhuis structure of the open (or non periodic) n-particle Toda lattice, introduced by Das and Okubo [7], and the Poisson quasi-Nijenhuis structure of the closed (or periodic) n-particle Toda lattice, described in our recent work [8].
Articolo in rivista - Articolo scientifico
Integrable systems; Poisson quasi-Nijenhuis manifolds; Toda lattices;
English
6-feb-2023
2023
186
April 2023
1
10
104773
embargoed_20250206
Falqui, G., Mencattini, I., Pedroni, M. (2023). Poisson quasi-Nijenhuis deformations of the canonical PN structure. JOURNAL OF GEOMETRY AND PHYSICS, 186(April 2023), 1-10 [10.1016/j.geomphys.2023.104773].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/415999
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