{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,16]],"date-time":"2026-01-16T02:44:07Z","timestamp":1768531447966,"version":"3.49.0"},"reference-count":35,"publisher":"MDPI AG","issue":"12","license":[{"start":{"date-parts":[[2022,12,7]],"date-time":"2022-12-07T00:00:00Z","timestamp":1670371200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Qassim University"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>We propose fundamental inequalities for contact pseudo-slant submanifolds of (\u03f5)-para Sasakian space form employing generalized normalized \u03b4-Casorati curvature. We characterize submanifolds for which equality cases hold and illustrate the main result with some applications. Further, we have considered a certain type of submanifold for a Ricci soliton and after computing its scalar curvature, developed an inequality to find correlations between intrinsic or extrinsic invariants.<\/jats:p>","DOI":"10.3390\/sym14122585","type":"journal-article","created":{"date-parts":[[2022,12,7]],"date-time":"2022-12-07T03:27:57Z","timestamp":1670383677000},"page":"2585","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["Some Basic Inequalities on (\u03f5)-Para Sasakian Manifold"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-5920-1227","authenticated-orcid":false,"given":"Majid","family":"Choudhary","sequence":"first","affiliation":[{"name":"Department of Mathematics, School of Sciences, Maulana Azad National Urdu University, Hyderabad 500032, India"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9652-0355","authenticated-orcid":false,"given":"Mohammad","family":"Khan","sequence":"additional","affiliation":[{"name":"Department of Computer Engineering, College of Computer, Qassim University, Buraydah 51452, Saudi Arabia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1713-6831","authenticated-orcid":false,"given":"Mohd","family":"Siddiqi","sequence":"additional","affiliation":[{"name":"Department of Mathematics, College of Science, Jazan University, Jazan 45142, Saudi Arabia"}]}],"member":"1968","published-online":{"date-parts":[[2022,12,7]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"568","DOI":"10.1007\/BF01236084","article-title":"Some pinching and classification theorems for minimal submanifolds","volume":"60","author":"Chen","year":"1993","journal-title":"Arch. 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