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 [7], and the Poisson quasi-Nijenhuis structure of the closed (or periodic) n-particle Toda lattice, described in our recent work [8].
(2023). Poisson quasi-Nijenhuis deformations of the canonical PN structure [journal article - articolo]. In JOURNAL OF GEOMETRY AND PHYSICS. Retrieved from https://hdl.handle.net/10446/246329
Poisson quasi-Nijenhuis deformations of the canonical PN structure
Pedroni, Marco
2023-01-01
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 [7], and the Poisson quasi-Nijenhuis structure of the closed (or periodic) n-particle Toda lattice, described in our recent work [8].File | Dimensione del file | Formato | |
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