{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,14]],"date-time":"2026-03-14T00:07:53Z","timestamp":1773446873750,"version":"3.50.1"},"reference-count":26,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2023,8,23]],"date-time":"2023-08-23T00:00:00Z","timestamp":1692748800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100004242","name":"Princess Nourah bint Abdulrahman University","doi-asserted-by":"publisher","award":["PNURSP2023R27"],"award-info":[{"award-number":["PNURSP2023R27"]}],"id":[{"id":"10.13039\/501100004242","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>The aim of this paper is to characterize a Riemannian 3-manifold M3 equipped with a semi-symmetric metric \u03be-connection \u2207\u02dc with \u03c1-Einstein and gradient \u03c1-Einstein solitons. The existence of a gradient \u03c1-Einstein soliton in an M3 admitting \u2207\u02dc is ensured by constructing a non-trivial example, and hence some of our results are verified. By using standard tensorial technique, we prove that the scalar curvature of (M3,\u2207\u02dc) satisfies the Poisson equation \u0394R=4(2\u2212\u03c3\u22126\u03c1)\u03c1.<\/jats:p>","DOI":"10.3390\/axioms12090809","type":"journal-article","created":{"date-parts":[[2023,8,23]],"date-time":"2023-08-23T08:20:30Z","timestamp":1692778830000},"page":"809","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["A Solitonic Study of Riemannian Manifolds Equipped with a Semi-Symmetric Metric \u03be-Connection"],"prefix":"10.3390","volume":"12","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-1175-6423","authenticated-orcid":false,"given":"Abdul","family":"Haseeb","sequence":"first","affiliation":[{"name":"Department of Mathematics, College of Science, Jazan University, Jazan 45142, Saudi Arabia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3882-4596","authenticated-orcid":false,"given":"Sudhakar Kumar","family":"Chaubey","sequence":"additional","affiliation":[{"name":"Section of Mathematics, Department of IT, University of Technology and Applied Sciences, Shinas 324, Oman"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2116-7382","authenticated-orcid":false,"given":"Fatemah","family":"Mofarreh","sequence":"additional","affiliation":[{"name":"Mathematical Science Department, Faculty of Science, Princess Nourah bint Abdulrahman University, Riyadh 11546, Saudi Arabia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9740-7207","authenticated-orcid":false,"given":"Abdullah Ali H.","family":"Ahmadini","sequence":"additional","affiliation":[{"name":"Department of Mathematics, College of Science, Jazan University, Jazan 45142, Saudi Arabia"}]}],"member":"1968","published-online":{"date-parts":[[2023,8,23]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"237","DOI":"10.1090\/conm\/071\/954419","article-title":"The Ricci Flow on Surfaces, Mathematics and General Relativity","volume":"71","author":"Hamilton","year":"1988","journal-title":"Contemp. 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