On three-dimensional Poisson quasi-Nijenhuis manifolds and Haantjes structures

E. Chuño Vizarreta; I. Mencattini; M. Pedroni

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arXiv · 2502.16559

On three-dimensional Poisson quasi-Nijenhuis manifolds and Haantjes structures

E. Chuño Vizarreta·I. Mencattini·M. Pedroni

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Abstract

In this note we first characterize Poisson quasi-Nijenhuis structures on three-dimensional oriented manifolds whose underlying Poisson tensor never vanishes. We then apply this result to show that each of these structures is (locally) a deformation of a PN structure and is involutive. Finally, we prove that every such three-dimensional Poisson quasi-Nijenhuis manifold is a Haantjes manifold and that it carries a generalized Lenard-Magri chain.

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E. Chuño Vizarreta, I. Mencattini, M. Pedroni. 2025-02-23. On three-dimensional Poisson quasi-Nijenhuis manifolds and Haantjes structures. https://arxiv.org/abs/2502.16559

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