"Warped product spaces with Ricci conditions" by SANG DEOK LEE, BYUNG HAK KIM et al.

<!DOCTYPE html> <html lang="en"> <head><script type='text/javascript' src='//cdnjs.cloudflare.com/ajax/libs/yui/3.6.0/yui/yui-min.js'></script><script type='text/javascript' src='//ajax.googleapis.com/ajax/libs/jquery/1.10.2/jquery.min.js'></script><script type='text/javascript' src='https://assets.adobedtm.com/4a848ae9611a/d0e96722185b/launch-d525bb0064d8.min.js'></script><script type='text/javascript' src=/assets/nr_browser_production.js></script>  <meta charset="utf-8"> <meta name="viewport" content="width=device-width"> <title> "Warped product spaces with Ricci conditions" by SANG DEOK LEE, BYUNG HAK KIM et al. </title>  <meta itemprop="name" content="Warped product spaces with Ricci conditions"> <meta property="og:title" content="Warped product spaces with Ricci conditions"> <meta name="twitter:title" content="Warped product spaces with Ricci conditions"> <meta property="article:author" content="SANG DEOK LEE"> <meta name="author" content="SANG DEOK LEE"> <meta property="article:author" content="BYUNG HAK KIM"> <meta name="author" content="BYUNG HAK KIM"> <meta property="article:author" content="JIN HYUK CHOI"> <meta name="author" content="JIN HYUK CHOI"> <meta name="robots" content="noodp, noydir"> <meta name="description" content="In this paper, we study the Ricci soliton in the Riemannian products$M=R^n \times B$ and warped products $M=R \times _f B$ of theEuclidean space and Riemannian manifolds, and the gradient Riccisoliton in the warped products $M=S^1 \times _f B$ of 1-dimensionalcircle and Riemannian manifolds. Moreover, we introduce the concept ofthe generalized Ricci soliton and we suggest the method of constructionof the Riemannian manifold $(M, g)$ with a Ricci soliton $g$.Finally, we also study the Lorentzian warped products with the Riccisoliton."> <meta itemprop="description" content="In this paper, we study the Ricci soliton in the Riemannian products$M=R^n \times B$ and warped products $M=R \times _f B$ of theEuclidean space and Riemannian manifolds, and the gradient Riccisoliton in the warped products $M=S^1 \times _f B$ of 1-dimensionalcircle and Riemannian manifolds. Moreover, we introduce the concept ofthe generalized Ricci soliton and we suggest the method of constructionof the Riemannian manifold $(M, g)$ with a Ricci soliton $g$.Finally, we also study the Lorentzian warped products with the Riccisoliton."> <meta name="twitter:description" content="In this paper, we study the Ricci soliton in the Riemannian products$M=R^n \times B$ and warped products $M=R \times _f B$ of theEuclidean space and Riemannian manifolds, and the gradient Riccisoliton in the warped products $M=S^1 \times _f B$ of 1-dimensionalcircle and Riemannian manifolds. Moreover, we introduce the concept ofthe generalized Ricci soliton and we suggest the method of constructionof the Riemannian manifold $(M, g)$ with a Ricci soliton $g$.Finally, we also study the Lorentzian warped products with the Riccisoliton."> <meta property="og:description" content="In this paper, we study the Ricci soliton in the Riemannian products$M=R^n \times B$ and warped products $M=R \times _f B$ of theEuclidean space and Riemannian manifolds, and the gradient Riccisoliton in the warped products $M=S^1 \times _f B$ of 1-dimensionalcircle and Riemannian manifolds. Moreover, we introduce the concept ofthe generalized Ricci soliton and we suggest the method of constructionof the Riemannian manifold $(M, g)$ with a Ricci soliton $g$.Finally, we also study the Lorentzian warped products with the Riccisoliton."> <meta name="keywords" content="Ricci curvature, warped product space, Ricci soliton"> <meta name="bepress_citation_journal_title" content="Turkish Journal of Mathematics"> <meta name="bepress_citation_firstpage" content="1365"> <meta name="bepress_citation_lastpage" content="1375"> <meta name="bepress_citation_author" content="LEE, SANG DEOK"> <meta name="bepress_citation_author" content="KIM, BYUNG HAK"> <meta name="bepress_citation_author" content="CHOI, JIN HYUK"> <meta name="bepress_citation_title" content="Warped product spaces with Ricci conditions"> <meta name="bepress_citation_date" content="2017"> <meta name="bepress_citation_volume" content="41"> <meta name="bepress_citation_issue" content="6">   <meta 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type="text/javascript" src="/assets/floatbox/floatbox.js"></script>     <div id="sub"> <div id="alpha"><div id='title' class='element'> <h1><a href='https://journals.tubitak.gov.tr/cgi/viewcontent.cgi?article=1842&context=math'>Warped product spaces with Ricci conditions</a></h1> </div> <div class='clear'></div> <div id='authors' class='element'> <h2 class='visually-hidden'>Authors</h2> <p class="author"><a href='https://journals.tubitak.gov.tr/do/search/?q=author%3A%22SANG%20DEOK%20LEE%22&start=0&context=26838904'><strong>SANG DEOK LEE</strong></a><br /> <a href='https://journals.tubitak.gov.tr/do/search/?q=author%3A%22BYUNG%20HAK%20KIM%22&start=0&context=26838904'><strong>BYUNG HAK KIM</strong></a><br /> <a href='https://journals.tubitak.gov.tr/do/search/?q=author%3A%22JIN%20HYUK%20CHOI%22&start=0&context=26838904'><strong>JIN HYUK CHOI</strong></a><br /> </p></div> <div class='clear'></div> <div id='abstract' class='element'> <h2 class='field-heading'>Abstract</h2> <p>In this paper, we study the Ricci soliton in the Riemannian products$M=R^n \times B$ and warped products $M=R \times _f B$ of theEuclidean space and Riemannian manifolds, and the gradient Riccisoliton in the warped products $M=S^1 \times _f B$ of 1-dimensionalcircle and Riemannian manifolds. Moreover, we introduce the concept ofthe generalized Ricci soliton and we suggest the method of constructionof the Riemannian manifold $(M, g)$ with a Ricci soliton $g$.Finally, we also study the Lorentzian warped products with the Riccisoliton.</p> </div> <div class='clear'></div> <div id='doi' class='element'> <h2 class='field-heading'>DOI</h2> <p>10.3906/mat-1606-49</p> </div> <div class='clear'></div> <div id='keywords' class='element'> <h2 class='field-heading'>Keywords</h2> <p>Ricci curvature, warped product space, Ricci soliton</p> </div> <div class='clear'></div> <div id='fpage' class='element'> <h2 class='field-heading'>First Page</h2> <p>1365</p> </div> <div class='clear'></div> <div id='lpage' class='element'> <h2 class='field-heading'>Last Page</h2> <p>1375</p> </div> <div class='clear'></div> <div id='recommended_citation' class='element'> <h2 class='field-heading'>Recommended Citation</h2>  <p class="citation"> LEE, SANG DEOK; KIM, BYUNG HAK; and CHOI, JIN HYUK (2017) "Warped product spaces with Ricci conditions," <em>Turkish Journal of Mathematics</em>: Vol. 41: No. 6, Article 1. <a href="https://doi.org/10.3906/mat-1606-49" >https://doi.org/10.3906/mat-1606-49</a> <br> Available at: https://journals.tubitak.gov.tr/math/vol41/iss6/1</p> </div> <div class='clear'></div> </div> </div> <div id='beta_7-3'>     <div class="aside download-button"> <a id="pdf" class="btn" href="https://journals.tubitak.gov.tr/cgi/viewcontent.cgi?article=1842&context=math" title="PDF (194 KB) opens in new window" target="_blank" > <i class="icon-download-alt" aria-hidden="true"></i> Download </a> </div>         <div id="article-stats" class="aside hidden"> <p class="article-downloads-wrapper hidden"><span id="article-downloads"></span> DOWNLOADS</p> <p class="article-stats-date hidden">Since January 28, 2022</p> <p class="article-plum-metrics"> <a href="https://plu.mx/plum/a/?repo_url=https://journals.tubitak.gov.tr/math/vol41/iss6/1" class="plumx-plum-print-popup 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