{"title":"On the structure of homogeneous local Poisson brackets","authors":"Guido Carlet , Matteo Casati","doi":"10.1016/j.difgeo.2025.102276","DOIUrl":null,"url":null,"abstract":"<div><div>We consider an arbitrary Dubrovin-Novikov bracket of degree <em>k</em>, namely a homogeneous degree <em>k</em> local Poisson bracket on the loop space of a smooth manifold <em>M</em> of dimension <em>n</em>, and show that <em>k</em> connections, defined by explicit linear combinations with constant coefficients of the standard connections associated with the Poisson bracket, are flat.</div></div>","PeriodicalId":51010,"journal":{"name":"Differential Geometry and its Applications","volume":"100 ","pages":"Article 102276"},"PeriodicalIF":0.7000,"publicationDate":"2025-08-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Differential Geometry and its Applications","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0926224525000518","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
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.
期刊介绍:
Differential Geometry and its Applications publishes original research papers and survey papers in differential geometry and in all interdisciplinary areas in mathematics which use differential geometric methods and investigate geometrical structures. The following main areas are covered: differential equations on manifolds, global analysis, Lie groups, local and global differential geometry, the calculus of variations on manifolds, topology of manifolds, and mathematical physics.