{"title":"ON CUBIC (\\alpha, \\beta)-METRICS IN FINSLER GEOMETRY","authors":"Hosein Tondro Vishkaei, A. Tayebi","doi":"10.22190/fumi220323030t","DOIUrl":null,"url":null,"abstract":"In this paper, we study the class of cubic (\\alpha, \\beta)-metrics. We show that every weakly Landsberg cubic (\\alpha, \\beta)-metric has vanishing S-curvature. Using it, we prove that cubic (\\alpha, \\beta)-metric is a weakly Landsberg metric if and only if it is a Berwald metric. This yields an extension of the Matsumoto's result for Landsberg cubic metric.","PeriodicalId":54148,"journal":{"name":"Facta Universitatis-Series Mathematics and Informatics","volume":"1 1","pages":""},"PeriodicalIF":0.5000,"publicationDate":"2022-08-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Facta Universitatis-Series Mathematics and Informatics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.22190/fumi220323030t","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
In this paper, we study the class of cubic (\alpha, \beta)-metrics. We show that every weakly Landsberg cubic (\alpha, \beta)-metric has vanishing S-curvature. Using it, we prove that cubic (\alpha, \beta)-metric is a weakly Landsberg metric if and only if it is a Berwald metric. This yields an extension of the Matsumoto's result for Landsberg cubic metric.
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