Existence of Finite Global Norm of Potential Vector Field in a Ricci Soliton

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 : 2023-07-05 DOI:10.1007/s40010-023-00839-7
Absos Ali Shaikh, Prosenjit Mandal, Chandan Kumar Mondal
{"title":"Existence of Finite Global Norm of Potential Vector Field in a Ricci Soliton","authors":"Absos Ali Shaikh,&nbsp;Prosenjit Mandal,&nbsp;Chandan Kumar Mondal","doi":"10.1007/s40010-023-00839-7","DOIUrl":null,"url":null,"abstract":"<div><p>In this paper, we present global norm of potential vector field in Ricci soliton. In particular, we deduce certain conditions so that the potential vector field has finite global norm in expanding Ricci soliton. In addition, we show that if the potential vector field has finite global norm in complete non-compact Ricci soliton having finite volume, then the scalar curvature becomes constant.</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":"2023-07-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","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/s40010-023-00839-7","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: 2

Abstract

In this paper, we present global norm of potential vector field in Ricci soliton. In particular, we deduce certain conditions so that the potential vector field has finite global norm in expanding Ricci soliton. In addition, we show that if the potential vector field has finite global norm in complete non-compact Ricci soliton having finite volume, then the scalar curvature becomes constant.

查看原文
分享 分享
微信好友 朋友圈 QQ好友 复制链接
本刊更多论文
Ricci孤子中位向量场有限全局范数的存在性
本文给出了Ricci孤子中位向量场的全局范数。特别地,我们推导了膨胀Ricci孤子中位向量场具有有限全局范数的若干条件。此外,我们还证明了在有限体积的完全非紧Ricci孤子中,如果势向量场具有有限全局范数,则标量曲率变为常数。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
求助全文
约1分钟内获得全文 去求助
来源期刊
CiteScore
2.60
自引率
0.00%
发文量
37
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
期刊最新文献
Double Sequences of Bi-complex Numbers Estimation of Crustal Tilting from Petrotectonic Interpretation of Mesozone Granitoid and its Marginal Parts, Eastern Dharwar Craton, India Transition Temperature versus Formula Mass of Selected High-TC Oxide Superconductors: A Step Closure to Room Temperature Superconductivity A Study on Countability in the Context of Multiset Topological Spaces On Machining Profile Accuracy in the Modified Electrochemical Machining Process
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
现在去查看 取消
×
提示
确定
0
微信
客服QQ
Book学术公众号 扫码关注我们
反馈
×
意见反馈
请填写您的意见或建议
请填写您的手机或邮箱
已复制链接
已复制链接
快去分享给好友吧!
我知道了
×
扫码分享
扫码分享
Book学术官方微信
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术
文献互助 智能选刊 最新文献 互助须知 联系我们:info@booksci.cn
Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。
Copyright © 2023 Book学术 All rights reserved.
ghs 京公网安备 11010802042870号 京ICP备2023020795号-1