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

2025/02/23 by E. Chuño Vizarreta, I. Mencattini, Vizarreta, E. Chuño +5 · 1 citation
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Geometric Analysis and Curvature Flows #Homotopy and Cohomology in Algebraic Topology #math.DG

paper · pdf · doi:10.48550/arxiv.2502.16559

openalex publication_date 2025/02/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Cited by

• Stäckel and Eisenhart lifts, Haantjes geometry and Gravitation

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