{"title":"ON WARPED PRODUCT MANIFOLDS ADMITTING τ-QUASI RICCI-HARMONIC METRICS","authors":"S. Günsen, L. Onat","doi":"10.22190/fumi211212023g","DOIUrl":null,"url":null,"abstract":"In this paper, we study warped product manifolds admitting $\\tau$-quasi Ricci-harmonic(RH) metrics. We prove that the metric of the fibre is harmonic Einstein when warped product metric is $\\tau$-quasi RH metric. We also provide some conditions for $M$ to be a harmonic Einstein manifold. Finally, we provide necessary and sufficient conditions for a metric $g$ to be $\\tau$-quasi RH metric by using a differential equation system.","PeriodicalId":54148,"journal":{"name":"Facta Universitatis-Series Mathematics and Informatics","volume":"49 1","pages":""},"PeriodicalIF":0.5000,"publicationDate":"2022-08-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Facta Universitatis-Series Mathematics and Informatics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.22190/fumi211212023g","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
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Abstract
In this paper, we study warped product manifolds admitting $\tau$-quasi Ricci-harmonic(RH) metrics. We prove that the metric of the fibre is harmonic Einstein when warped product metric is $\tau$-quasi RH metric. We also provide some conditions for $M$ to be a harmonic Einstein manifold. Finally, we provide necessary and sufficient conditions for a metric $g$ to be $\tau$-quasi RH metric by using a differential equation system.
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