{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,22]],"date-time":"2026-01-22T17:33:25Z","timestamp":1769103205704,"version":"3.49.0"},"reference-count":35,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2024,5,30]],"date-time":"2024-05-30T00:00:00Z","timestamp":1717027200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>In this article, we study the Ricci soliton on slant submanifolds of trans-Sasakian manifolds with a quarter symmetric non-metric connection. Moreover, we derive a lower-bound-type inequality for the slant submanifolds of trans-Sasakian manifolds with a quarter symmetric non-metric connection in terms of gradient Ricci solitons. We also characterize anti-invariant, invariant, quasi-umbilical submanifolds of trans-Sasakian manifolds with a quarter symmetric non-metric connection for which the same inequality case holds. Finally, we deduce the above inequalities in terms of a scalar concircular field on submanifolds of trans-Sasakian manifolds with a quarter symmetric non-metric connection.<\/jats:p>","DOI":"10.3390\/axioms13060370","type":"journal-article","created":{"date-parts":[[2024,5,30]],"date-time":"2024-05-30T06:08:14Z","timestamp":1717049294000},"page":"370","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Solitonical Inequality on Submanifolds in Trans-Sasakian Manifolds Coupled with a Slant Factor"],"prefix":"10.3390","volume":"13","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 114, Jazan 45142, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Rawan","family":"Bossly","sequence":"additional","affiliation":[{"name":"Department of Mathematics, College of Science, Jazan University, P.O. Box 114, Jazan 45142, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2024,5,30]]},"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. Math. Am. Math. Soc."},{"key":"ref_2","first-page":"355","article-title":"Inequalities for gradient Einstein and Ricci solitons","volume":"35","author":"Blaga","year":"2020","journal-title":"Facta Univ. Ser. Math. 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