{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,25]],"date-time":"2026-08-25T06:48:53Z","timestamp":1787640533682,"version":"build-2736575974"},"reference-count":46,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2023,8,17]],"date-time":"2023-08-17T00:00:00Z","timestamp":1692230400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Princess Nourah bint Abdulrahman University","award":["PNURSP2023R27"],"award-info":[{"award-number":["PNURSP2023R27"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>In this paper, we investigate the geometrical axioms of Riemannian submersions in the context of the \u03b7-Ricci\u2013Yamabe soliton (\u03b7-RY soliton) with a potential field. We give the categorization of each fiber of Riemannian submersion as an \u03b7-RY soliton, an \u03b7-Ricci soliton, and an \u03b7-Yamabe soliton. Additionally, we consider the many circumstances under which a target manifold of Riemannian submersion is an \u03b7-RY soliton, an \u03b7-Ricci soliton, an \u03b7-Yamabe soliton, or a quasi-Yamabe soliton. We deduce a Poisson equation on a Riemannian submersion in a specific scenario if the potential vector field \u03c9 of the soliton is of gradient type =:grad(\u03b3) and provide some examples of an \u03b7-RY soliton, which illustrates our finding. Finally, we explore a number theoretic approach to Riemannian submersion with totally geodesic fibers.<\/jats:p>","DOI":"10.3390\/axioms12080796","type":"journal-article","created":{"date-parts":[[2023,8,17]],"date-time":"2023-08-17T10:47:02Z","timestamp":1692269222000},"page":"796","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":13,"title":["\u03b7-Ricci\u2013Yamabe Solitons along Riemannian Submersions"],"prefix":"10.3390","volume":"12","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-1713-6831","authenticated-orcid":false,"given":"Mohd Danish","family":"Siddiqi","sequence":"first","affiliation":[{"name":"Department of Mathematics, College of Science, Jazan University, P.O. Box 277, Jazan 45142, Saudi Arabia"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"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"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2334-6955","authenticated-orcid":false,"given":"Mehmet Akif","family":"Akyol","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Arts and Sciences, Bingol University, Bingol 12000, Turkey"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Ali H.","family":"Hakami","sequence":"additional","affiliation":[{"name":"Department of Mathematics, College of Science, Jazan University, P.O. Box 277, Jazan 45142, Saudi Arabia"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2023,8,17]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"20","DOI":"10.2307\/1969989","article-title":"The embedding problem for Riemannian manifolds","volume":"63","author":"Nash","year":"1956","journal-title":"Ann. Math."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"189","DOI":"10.1007\/BF01942061","article-title":"Stability and isolation phenomena for Yang-mills fields","volume":"79","author":"Bourguignon","year":"1981","journal-title":"Commun. Math. Phys."},{"key":"ref_3","unstructured":"Bourguignon, J.P., and Lawson, H.B. (1989). A mathematician\u2019s visit to Kaluza-Klein theory. Rend. Semin. Mat. Torino Fasc. 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