{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,1]],"date-time":"2026-07-01T08:43:40Z","timestamp":1782895420056,"version":"3.54.5"},"reference-count":26,"publisher":"MDPI AG","issue":"10","license":[{"start":{"date-parts":[[2023,10,8]],"date-time":"2023-10-08T00:00:00Z","timestamp":1696723200000},"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 the present article, we consider submanifolds in golden Riemannian manifolds with constant golden sectional curvature. On such submanifolds, we prove geometric inequalities for the Casorati curvatures. The submanifolds meeting the equality cases are also described.<\/jats:p>","DOI":"10.3390\/axioms12100952","type":"journal-article","created":{"date-parts":[[2023,10,9]],"date-time":"2023-10-09T06:16:48Z","timestamp":1696832208000},"page":"952","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["Inequalities for the Generalized Normalized \u03b4-Casorati Curvatures of Submanifolds in Golden Riemannian Manifolds"],"prefix":"10.3390","volume":"12","author":[{"given":"Majid Ali","family":"Choudhary","sequence":"first","affiliation":[{"name":"Department of Mathematics, School of Sciences, Maulana Azad National Urdu University (Central University), Hyderabad 500032, India"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3782-2983","authenticated-orcid":false,"given":"Ion","family":"Mihai","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Mathematics and Computer Science, University of Bucharest, 010014 Bucharest, Romania"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2023,10,8]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"199","DOI":"10.2996\/kmj\/1138846118","article-title":"Polynomial structures on manifolds","volume":"22","author":"Goldberg","year":"1970","journal-title":"Kodai Math. 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