{"title":"Almost Ricci-Bourguignon soliton on warped product space","authors":"Santosh Kumar, Pankaj Kumar, Buddhadev Pal","doi":"10.1016/S0034-4877(23)00058-7","DOIUrl":null,"url":null,"abstract":"<div><p>The purpose of this article is to study the almost Ricci-Bourguignon soliton<span> on warped product space. Some results for solenoidal and concurrent vector fields are obtained on warped product space with almost Ricci-Bourguignon soliton. We provide the relation between the warped manifold and its base manifold (fiber manifold) for an almost Ricci-Bourguignon soliton. We also generalize the Bochner formula in warped product space. Next, we study the Riemannian map whose total manifold admits an almost Ricci-Bourguignon soliton. We find the condition for a kernel of Riemannian map to become an almost Ricci-Bourguignon soliton. Moreover, we give an example for almost Ricci-Bourguignon soliton on warped product space.</span></p></div>","PeriodicalId":49630,"journal":{"name":"Reports on Mathematical Physics","volume":"92 1","pages":"Pages 99-115"},"PeriodicalIF":1.0000,"publicationDate":"2023-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Reports on Mathematical Physics","FirstCategoryId":"101","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0034487723000587","RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"PHYSICS, MATHEMATICAL","Score":null,"Total":0}
引用次数: 0
Abstract
The purpose of this article is to study the almost Ricci-Bourguignon soliton on warped product space. Some results for solenoidal and concurrent vector fields are obtained on warped product space with almost Ricci-Bourguignon soliton. We provide the relation between the warped manifold and its base manifold (fiber manifold) for an almost Ricci-Bourguignon soliton. We also generalize the Bochner formula in warped product space. Next, we study the Riemannian map whose total manifold admits an almost Ricci-Bourguignon soliton. We find the condition for a kernel of Riemannian map to become an almost Ricci-Bourguignon soliton. Moreover, we give an example for almost Ricci-Bourguignon soliton on warped product space.
期刊介绍:
Reports on Mathematical Physics publish papers in theoretical physics which present a rigorous mathematical approach to problems of quantum and classical mechanics and field theories, relativity and gravitation, statistical physics, thermodynamics, mathematical foundations of physical theories, etc. Preferred are papers using modern methods of functional analysis, probability theory, differential geometry, algebra and mathematical logic. Papers without direct connection with physics will not be accepted. Manuscripts should be concise, but possibly complete in presentation and discussion, to be comprehensible not only for mathematicians, but also for mathematically oriented theoretical physicists. All papers should describe original work and be written in English.