{"title":"Сurvilinear Three-Webs with Automorphisms","authors":"A. M. Shelekhov","doi":"10.3103/s1066369x24700464","DOIUrl":null,"url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>A general form of the equation of a curvilinear three-web admitting a one-parameter family of automorphisms (<span>\\(AW\\)</span>-webs) is found. It is proved that the trajectories of automorphisms of an <span>\\(AW\\)</span>-web are geodesics of its Chern connection. All <span>\\(AW\\)</span>-webs are found for which one of the covariant derivatives of curvature is zero.</p>","PeriodicalId":46110,"journal":{"name":"Russian Mathematics","volume":"2 1","pages":""},"PeriodicalIF":0.5000,"publicationDate":"2024-09-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Russian Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.3103/s1066369x24700464","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
A general form of the equation of a curvilinear three-web admitting a one-parameter family of automorphisms (\(AW\)-webs) is found. It is proved that the trajectories of automorphisms of an \(AW\)-web are geodesics of its Chern connection. All \(AW\)-webs are found for which one of the covariant derivatives of curvature is zero.
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