{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,22]],"date-time":"2025-10-22T23:10:25Z","timestamp":1761174625227,"version":"build-2065373602"},"reference-count":42,"publisher":"MDPI AG","issue":"10","license":[{"start":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T00:00:00Z","timestamp":1760054400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Deanship of Scientific Research at Imam Mohammad Ibn Saud Islamic University","award":["IMSIU-DDRSP2502"],"award-info":[{"award-number":["IMSIU-DDRSP2502"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>In this paper, we study Z-solitons and gradient Z-solitons on \u03b1-cosymplectic manifolds. The soliton structure is defined by the generalized tensor Z=S+\u03b2g, where S denotes the Ricci tensor, g the metric tensor, and \u03b2 a smooth function. We investigate the geometric implications of Z-solitons under various curvature conditions, with a focus on the interplay between the Z-tensor and the Q-curvature tensor, as well as the case of Z-recurrent \u03b1-cosymplectic manifolds. Our classification results establish that such manifolds can be Einstein, \u03b7-Einstein, or of constant curvature. Finally, we construct a concrete five-dimensional example of an \u03b1-cosymplectic manifold that admits a Z-soliton structure, thereby illustrating the theoretical framework.<\/jats:p>","DOI":"10.3390\/axioms14100759","type":"journal-article","created":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T13:47:08Z","timestamp":1760104028000},"page":"759","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Z-Solitons and Gradient Z-Solitons on \u03b1-Cosymplectic Manifolds"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-7885-1492","authenticated-orcid":false,"given":"Mustafa","family":"Yildirim","sequence":"first","affiliation":[{"name":"Department of Mathematics, Faculty of Science and Art, Aksaray University, 68100 Aksaray, T\u00fcrkiye"}]},{"given":"Mehmet","family":"Akif Akyol","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Engineering and Natural Sciences, U\u015fak University, 64000 U\u015fak, T\u00fcrkiye"}]},{"given":"Majid Ali","family":"Choudhary","sequence":"additional","affiliation":[{"name":"Department of Mathematics, School of Sciences, Maulana Azad National Urdu University, Hyderabad 500032, India"}]},{"ORCID":"https:\/\/orcid.org\/0009-0003-7359-484X","authenticated-orcid":false,"given":"Foued","family":"Aloui","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Statistics, College of Science, Imam Mohammad Ibn Saud Islamic University (IMSIU), P.O. Box 65892, Riyadh 11566, Saudi Arabia"}]}],"member":"1968","published-online":{"date-parts":[[2025,10,10]]},"reference":[{"key":"ref_1","first-page":"255","article-title":"Three-manifolds with positive Ricci curvature","volume":"17","author":"Hamilton","year":"1982","journal-title":"J. Differ. Geom."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"237","DOI":"10.1090\/conm\/071\/954419","article-title":"The Ricci flow on surfaces","volume":"71","author":"Hamilton","year":"1988","journal-title":"Contemp. Math."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"758","DOI":"10.1016\/0550-3213(96)00341-0","article-title":"A class of compact and non-compact quasi-Einstein metrics and the renormalizability properties","volume":"478","author":"Chave","year":"1996","journal-title":"Nucl. Phys. 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