{"title":"On the Equivalence of Two Non-Riemannian Curvatures in Warped Product Finsler Metrics","authors":"Bankteshwar Tiwari, Ranadip Gangopadhyay, Anjali Shriwastawa","doi":"10.1007/s40010-023-00817-z","DOIUrl":null,"url":null,"abstract":"<div><p>In this paper we discuss the Busemann-Hausdorff volume form and Holmes-Thompson volume form for the warped product Finsler metrics. With the help of these volume forms we obtain the <i>E</i>-curvature and the <i>S</i>-curvature for this class of metrics. Further, we show that the notion of isotropic <i>E</i>-curvature and isotropic <i>S</i>-curvature are equivalent for this class of metrics.</p></div>","PeriodicalId":744,"journal":{"name":"Proceedings of the National Academy of Sciences, India Section A: Physical Sciences","volume":null,"pages":null},"PeriodicalIF":0.8000,"publicationDate":"2023-02-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Proceedings of the National Academy of Sciences, India Section A: Physical Sciences","FirstCategoryId":"103","ListUrlMain":"https://link.springer.com/article/10.1007/s40010-023-00817-z","RegionNum":4,"RegionCategory":"综合性期刊","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MULTIDISCIPLINARY SCIENCES","Score":null,"Total":0}
引用次数: 1
Abstract
In this paper we discuss the Busemann-Hausdorff volume form and Holmes-Thompson volume form for the warped product Finsler metrics. With the help of these volume forms we obtain the E-curvature and the S-curvature for this class of metrics. Further, we show that the notion of isotropic E-curvature and isotropic S-curvature are equivalent for this class of metrics.
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