{"title":"Gronwall's conjecture for 3-webs with two pencils of lines","authors":"Sergey I. Agafonov","doi":"10.1016/j.difgeo.2023.102071","DOIUrl":null,"url":null,"abstract":"<div><p>We prove the old-standing Gronwall conjecture in the particular case of linear 3-webs whose 2 foliations are 2 pencils of lines. For a non-hexagonal 3-web, we also introduce a family of projective torsion-free Cartan connections, the web leaves being geodesics for each member of the family, and give a web linearization criterion.</p></div>","PeriodicalId":51010,"journal":{"name":"Differential Geometry and its Applications","volume":"91 ","pages":"Article 102071"},"PeriodicalIF":0.6000,"publicationDate":"2023-10-13","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/S0926224523000979","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 prove the old-standing Gronwall conjecture in the particular case of linear 3-webs whose 2 foliations are 2 pencils of lines. For a non-hexagonal 3-web, we also introduce a family of projective torsion-free Cartan connections, the web leaves being geodesics for each member of the family, and give a web linearization criterion.
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.
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