On the structure of homogeneous local Poisson brackets

2025/05/02 by Guido Carlet, Carlet, Guido, Matteo Casati +1 · 1 citation
Mathematics · #37K25 (Secondary) #53D17 (primary) #Advanced Algebra and Geometry #Advanced Topics in Algebra #Differential Geometry (math.DG) #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Mathematics #FOS: Physical sciences #Homotopy and Cohomology in Algebraic Topology #Mathematical Physics (math-ph)

paper · pdf · doi:10.48550/arxiv.2505.01138

openalex publication_date 2025/05/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider an arbitrary Dubrovin-Novikov bracket of degree k, namely a homogeneous degree k local Poisson bracket on the loop space of a smooth manifold M of dimension n, and show that k connections, defined by explicit linear combinations with constant coefficients of the standard connections associated with the Poisson bracket, are flat.

Citations

• On deformations of one-dimensional Poisson structures of hydrodynamic type with degenerate metric
• Jacobi Structures of Evolutionary Partial Differential Equations
• Normal forms of hierarchies of integrable PDEs, Frobenius manifolds and Gromov - Witten invariants
• On Deformation of Poisson Manifolds of Hydrodynamic Type
• A Darboux theorem for Hamiltonian operators in the formal calculus of variations

Cited by

• Compatible pairs of Hamiltonian operators of the first and third orders

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