Poisson quasi-Nijenhuis deformations of the canonical PN structure

被引：1

作者：

Falqui, G. ^{[1
,4
,5
]}

Mencattini, I. ^{[2
]}

Pedroni, M. ^{[3
,5
]}

机构：

[1] Univ Milano Bicocca, Dipartimento Matemat & Applicazioni, Bicocca, Italy

[2] Univ Sao Paulo, Inst Ciencias Matemat & Computacao, Sao Paulo, Brazil

[3] Univ Bergamo, Dipartimento Ingegnena Gestionale, Informaz & Prod, Bergamo, Italy

[4] via Bonomea 265, I-34136 Sissa, Italy

[5] Sez Milano Bicocca, INFN, Piazza Sci 3, I-20126 Milan, Italy

来源：

JOURNAL OF GEOMETRY AND PHYSICS | 2023年 / 186卷

基金：

欧盟地平线“2020”;

关键词：

Poisson quasi-Nijenhuis manifolds; Integrable systems; Toda lattices; HAMILTONIAN-STRUCTURE; TODA SYSTEMS;

D O I：

10.1016/j.geomphys.2023.104773

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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].(c) 2023 Elsevier B.V. All rights reserved.

引用

页数：10

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