翘曲积Finsler度量中两个非黎曼曲率的等价性

IF 0.8 4区综合性期刊 Q3 MULTIDISCIPLINARY SCIENCES

Proceedings of the National Academy of Sciences, India Section A: Physical Sciences Pub Date : 2023-02-17 DOI:10.1007/s40010-023-00817-z

Bankteshwar Tiwari, Ranadip Gangopadhyay, Anjali Shriwastawa

{"title":"翘曲积Finsler度量中两个非黎曼曲率的等价性","authors":"Bankteshwar Tiwari, Ranadip Gangopadhyay, Anjali Shriwastawa","doi":"10.1007/s40010-023-00817-z","DOIUrl":null,"url":null,"abstract":"<div>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.</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":"{\"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>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.</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}","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

摘要

本文讨论了翘曲积Finsler度量的Busemann-Hausdorff体积形式和Holmes-Thompson体积形式。借助这些体积形式，我们得到了这类度量的e曲率和s曲率。进一步，我们证明了各向同性e曲率和各向同性s曲率的概念对于这类度量是等价的。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

On the Equivalence of Two Non-Riemannian Curvatures in Warped Product Finsler Metrics

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.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

Proceedings of the National Academy of Sciences, India Section A: Physical Sciences 综合性期刊-综合性期刊

CiteScore

2.60

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： To promote research in all the branches of Science & Technology; and disseminate the knowledge and advancements in Science & Technology