Diameter Estimation of \((m,\rho )\)-Quasi Einstein Manifolds

IF 0.8 4区 综合性期刊 Q3 MULTIDISCIPLINARY SCIENCES
Absos Ali Shaikh, Prosenjit Mandal, Chandan Kumar Mondal
{"title":"Diameter Estimation of \\((m,\\rho )\\)-Quasi Einstein Manifolds","authors":"Absos Ali Shaikh,&nbsp;Prosenjit Mandal,&nbsp;Chandan Kumar Mondal","doi":"10.1007/s40010-024-00899-3","DOIUrl":null,"url":null,"abstract":"<div><p>This paper aims to study the <span>\\((m,\\rho )\\)</span>-quasi Einstein manifold. This article shows that a complete and connected Riemannian manifold under certain conditions becomes compact. Also, we have determined an upper bound of the diameter for such a manifold. It is also exhibited that the potential function agrees with the Hodge-de Rham potential up to a real constant in an <span>\\((m,\\rho )\\)</span>-quasi Einstein manifold. Later, some triviality and integral conditions are established for a non-compact complete <span>\\((m,\\rho )\\)</span>-quasi Einstein manifold having finite volume. Finally, it is proved that with some certain constraints, a complete Riemannian manifold admits finite fundamental group. Furthermore, some conditions for compactness criteria have also been deduced.</p></div>","PeriodicalId":744,"journal":{"name":"Proceedings of the National Academy of Sciences, India Section A: Physical Sciences","volume":"94 5","pages":"513 - 518"},"PeriodicalIF":0.8000,"publicationDate":"2024-11-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","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/s40010-024-00899-3","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: 0

Abstract

This paper aims to study the \((m,\rho )\)-quasi Einstein manifold. This article shows that a complete and connected Riemannian manifold under certain conditions becomes compact. Also, we have determined an upper bound of the diameter for such a manifold. It is also exhibited that the potential function agrees with the Hodge-de Rham potential up to a real constant in an \((m,\rho )\)-quasi Einstein manifold. Later, some triviality and integral conditions are established for a non-compact complete \((m,\rho )\)-quasi Einstein manifold having finite volume. Finally, it is proved that with some certain constraints, a complete Riemannian manifold admits finite fundamental group. Furthermore, some conditions for compactness criteria have also been deduced.

准爱因斯坦流形的直径估计
本文旨在研究准爱因斯坦流形。本文表明,在某些条件下,一个完整且连通的黎曼流形会变得紧凑。同时,我们还确定了这样一个流形的直径上限。本文还证明了在\((m,\rho )\)准爱因斯坦流形中,势函数与霍奇-德-拉姆势一致,直到一个实常数。随后,建立了具有有限体积的非紧凑完整的((m,\rho ))准爱因斯坦流形的一些三性和积分性条件。最后,证明了在某些约束条件下,完全黎曼流形具有有限基群。此外,还推导出了紧凑性标准的一些条件。
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 求助全文
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
×
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
确定
请完成安全验证×
copy
已复制链接
快去分享给好友吧!
我知道了
右上角分享
点击右上角分享
0
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 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术官方微信