{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,25]],"date-time":"2026-01-25T21:07:44Z","timestamp":1769375264530,"version":"3.49.0"},"reference-count":64,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2021,11,16]],"date-time":"2021-11-16T00:00:00Z","timestamp":1637020800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["12101168"],"award-info":[{"award-number":["12101168"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>The outline of this research article is to initiate the development of a \u2217-conformal \u03b7-Ricci\u2013Yamabe soliton in \u03b1-Cosymplectic manifolds according to the quarter-symmetric metric connection. Here, we have established some curvature properties of \u03b1-Cosymplectic manifolds in regard to the quarter-symmetric metric connection. Further, the attributes of the soliton when the manifold gratifies a quarter-symmetric metric connection have been displayed in this article. Later, we picked up the Laplace equation from \u2217-conformal \u03b7-Ricci\u2013Yamabe soliton equation when the potential vector field \u03be of the soliton is of gradient type, admitting quarter-symmetric metric connection. Next, we evolved the nature of the soliton when the vector field\u2019s conformal killing reveals a quarter-symmetric metric connection. We show an example of a 5-dimensional \u03b1-cosymplectic metric as a \u2217-conformal \u03b7-Ricci\u2013Yamabe soliton acknowledges quarter-symmetric metric connection to prove our results.<\/jats:p>","DOI":"10.3390\/sym13112189","type":"journal-article","created":{"date-parts":[[2021,11,17]],"date-time":"2021-11-17T21:32:07Z","timestamp":1637184727000},"page":"2189","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":11,"title":["Geometry of \u03b1-Cosymplectic Metric as \u2217-Conformal \u03b7-Ricci\u2013Yamabe Solitons Admitting Quarter-Symmetric Metric Connection"],"prefix":"10.3390","volume":"13","author":[{"given":"Pengfei","family":"Zhang","sequence":"first","affiliation":[{"name":"College of Teacher Education, Harbin Normal University, Harbin 150025, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1614-3228","authenticated-orcid":false,"given":"Yanlin","family":"Li","sequence":"additional","affiliation":[{"name":"School of Mathematics, Hangzhou Normal University, Hangzhou 311121, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2236-8482","authenticated-orcid":false,"given":"Soumendu","family":"Roy","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Jadavpur University, Kolkata 700032, India"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2601-3788","authenticated-orcid":false,"given":"Santu","family":"Dey","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Bidhan Chandra College, Asansol-4, Rishra 713304, India"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2021,11,16]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"255","DOI":"10.4310\/jdg\/1214436922","article-title":"Three Manifold with positive Ricci curvature","volume":"17","author":"Hamilton","year":"1982","journal-title":"J. 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