{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T02:15:41Z","timestamp":1760148941429,"version":"build-2065373602"},"reference-count":11,"publisher":"MDPI AG","issue":"7","license":[{"start":{"date-parts":[[2023,6,21]],"date-time":"2023-06-21T00:00:00Z","timestamp":1687305600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"National Natural Science Foundation of China","award":["11961061","11461064","12071283"],"award-info":[{"award-number":["11961061","11461064","12071283"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>In this paper, we study Kropina metrics with isotropic scalar curvature. First, we obtain the expressions of Ricci curvature tensor and scalar curvature. Then, we characterize the Kropina metrics with isotropic scalar curvature on by tensor analysis.<\/jats:p>","DOI":"10.3390\/axioms12070611","type":"journal-article","created":{"date-parts":[[2023,6,21]],"date-time":"2023-06-21T02:30:51Z","timestamp":1687314651000},"page":"611","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Kropina Metrics with Isotropic Scalar Curvature"],"prefix":"10.3390","volume":"12","author":[{"given":"Liulin","family":"Liu","sequence":"first","affiliation":[{"name":"College of Mathematics and Systems Science, Xinjiang University, Urumqi 830017, China"}]},{"given":"Xiaoling","family":"Zhang","sequence":"additional","affiliation":[{"name":"College of Mathematics and Systems Science, Xinjiang University, Urumqi 830017, China"}]},{"given":"Lili","family":"Zhao","sequence":"additional","affiliation":[{"name":"School of Mathematical Sciences, Shanghai Jiao Tong University, Shanghai 200240, China"}]}],"member":"1968","published-online":{"date-parts":[[2023,6,21]]},"reference":[{"key":"ref_1","first-page":"271","article-title":"Sur les espaces de Finsler A courbures sectionnelles constantes","volume":"74","year":"1988","journal-title":"Bulletins de l\u2019Acad\u00e9mie Royale de Belgique"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"221","DOI":"10.1007\/s11856-012-0036-x","article-title":"A class of Einstein (\u03b1,\u03b2)-metrics","volume":"192","author":"Cheng","year":"2012","journal-title":"Isr. J. Math."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"80","DOI":"10.1016\/j.difgeo.2012.10.011","article-title":"On Einstein Kropina metrics","volume":"31","author":"Zhang","year":"2013","journal-title":"Differ. Geom. Appl."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"393","DOI":"10.1016\/j.difgeo.2013.03.001","article-title":"On Kropina metrics of scalar flag curvature","volume":"31","author":"Xia","year":"2013","journal-title":"Differ. Geom. Appl."},{"key":"ref_5","first-page":"705","article-title":"On projective Ricci flat Kropina metrics","volume":"37","author":"Cheng","year":"2017","journal-title":"J. Math."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"530","DOI":"10.4153\/CMB-2014-063-4","article-title":"Ricci curvature tensor and non-Riemannian quantities","volume":"58","author":"Li","year":"2015","journal-title":"Can. Math. Bull."},{"key":"ref_7","first-page":"41","article-title":"On the Ricci tensors of particular Finsler spaces","volume":"14","author":"Shimada","year":"1977","journal-title":"J. Korean Math. Soc."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"1665","DOI":"10.1016\/j.geomphys.2010.05.016","article-title":"On Ricci tensors of Randers metrics","volume":"60","author":"Tayebi","year":"2010","journal-title":"J. Geom. Phys."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"907","DOI":"10.1515\/ms-2017-0154","article-title":"On generalized 4-th root metrics of isotropic scalar curvature","volume":"68","author":"Tayebi","year":"2018","journal-title":"Math. Slovaca"},{"key":"ref_10","first-page":"329","article-title":"On conformally flat polynomial (\u03b1,\u03b2)-metrics with weakly isotropic scalar curvature","volume":"56","author":"Chen","year":"2019","journal-title":"J. Korean Math. Soc."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"1850003","DOI":"10.1142\/S0129167X18500039","article-title":"Sprays of isotropic curvature","volume":"29","author":"Li","year":"2018","journal-title":"Int. J. Math."}],"container-title":["Axioms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2075-1680\/12\/7\/611\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T19:57:34Z","timestamp":1760126254000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2075-1680\/12\/7\/611"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,6,21]]},"references-count":11,"journal-issue":{"issue":"7","published-online":{"date-parts":[[2023,7]]}},"alternative-id":["axioms12070611"],"URL":"https:\/\/doi.org\/10.3390\/axioms12070611","relation":{},"ISSN":["2075-1680"],"issn-type":[{"type":"electronic","value":"2075-1680"}],"subject":[],"published":{"date-parts":[[2023,6,21]]}}}