{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,4]],"date-time":"2026-03-04T15:19:39Z","timestamp":1772637579839,"version":"3.50.1"},"reference-count":30,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2026,2,27]],"date-time":"2026-02-27T00:00:00Z","timestamp":1772150400000},"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-DDRSP2602"],"award-info":[{"award-number":["IMSIU-DDRSP2602"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>In this paper, we establish sharp pinching inequalities that relate the generalized \u03b4-Casorati curvatures to the normalized scalar curvature of submanifolds immersed in K\u00e4hler product manifolds endowed with a quarter-symmetric metric connection. The results are obtained for a broad range of geometric configurations, encompassing several important classes of submanifolds. Moreover, we prove that the derived inequalities are optimal by completely characterizing the submanifolds for which equality holds, showing that these cases correspond precisely to invariantly quasi-umbilical submanifolds with trivial normal connection.<\/jats:p>","DOI":"10.3390\/axioms15030168","type":"journal-article","created":{"date-parts":[[2026,2,27]],"date-time":"2026-02-27T15:52:38Z","timestamp":1772207558000},"page":"168","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Curvature Bounds and Casorati Pinching for Submanifolds in K\u00e4hler Product Manifolds"],"prefix":"10.3390","volume":"15","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-9343-0725","authenticated-orcid":false,"given":"Md","family":"Aquib","sequence":"first","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"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ibrahim","family":"Al-Dayel","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"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Mohd","family":"Aslam","sequence":"additional","affiliation":[{"name":"Department of Computer Science and Information Technology, Maulana Azad National Urdu University, Hyderabad 500032, Telangana, India"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5054-8865","authenticated-orcid":false,"given":"O\u011fuzhan","family":"Bahad\u0131r","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Sciences, Kahramanmaras Sutcu Imam University, Kahramanmaras 46100, Turkey"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2026,2,27]]},"reference":[{"key":"ref_1","first-page":"8","article-title":"CR-submanifolds of K\u00e4hlerian product manifolds","volume":"12","author":"Atceken","year":"2007","journal-title":"Balk. J. Geom. 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