{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T01:47:00Z","timestamp":1760233620390,"version":"build-2065373602"},"reference-count":26,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2021,1,29]],"date-time":"2021-01-29T00:00:00Z","timestamp":1611878400000},"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":["Fast-Track Funding Programm"],"award-info":[{"award-number":["Fast-Track Funding Programm"]}],"id":[{"id":"10.13039\/501100004242","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>In this paper, we give some classifications of the k-Yamabe solitons on the hypersurfaces of the Euclidean spaces from the vector field point of view. In several results on k-Yamabe solitons with a concurrent vector field on submanifolds in Riemannian manifolds, is proved that a k-Yamabe soliton (Mn,g,vT,\u03bb) on a hypersurface in the Euclidean space Rn+1 is contained either in a hypersphere or a hyperplane. We provide an example to support this study and all of the results in this paper can be implemented to Yamabe solitons for k-curvature with k=1.<\/jats:p>","DOI":"10.3390\/sym13020222","type":"journal-article","created":{"date-parts":[[2021,1,29]],"date-time":"2021-01-29T09:25:22Z","timestamp":1611912322000},"page":"222","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["Geometry of k-Yamabe Solitons on Euclidean Spaces and Its Applications to Concurrent Vector Fields"],"prefix":"10.3390","volume":"13","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-6053-3031","authenticated-orcid":false,"given":"Akram","family":"Ali","sequence":"first","affiliation":[{"name":"Department of Mathematics, College of Science, King Khalid University, Abha 62529, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"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":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2269-718X","authenticated-orcid":false,"given":"Pi\u015fcoran","family":"Laurian-Ioan","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Computer Science Victoriei 76, North University Center of Baia Mare Technical University of Cluj Napoca, 430122 Baia Mare, Romania"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7135-0559","authenticated-orcid":false,"given":"Nadia","family":"Alluhaibi","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Science and Arts College, Rabigh Campus, King Abdulaziz University, Jeddah 21911, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2021,1,29]]},"reference":[{"key":"ref_1","unstructured":"Besse, A.L. 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