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arXiv · 2505.01138

On the structure of homogeneous local Poisson brackets

Guido Carlet·Matteo Casati
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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.

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Guido Carlet, Matteo Casati. 2025-05-02. On the structure of homogeneous local Poisson brackets. https://arxiv.org/abs/2505.01138

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