{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T01:13:05Z","timestamp":1760145185121,"version":"build-2065373602"},"reference-count":45,"publisher":"MDPI AG","issue":"7","license":[{"start":{"date-parts":[[2024,7,4]],"date-time":"2024-07-04T00:00:00Z","timestamp":1720051200000},"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 (IMSIU)","award":["IMSIU-RG23036"],"award-info":[{"award-number":["IMSIU-RG23036"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>This article explores the Ricci tensor of slant submanifolds within locally metallic product space forms equipped with a semi-symmetric metric connection (SSMC). Our investigation includes the derivation of the Chen\u2013Ricci inequality and an in-depth analysis of its equality case. More precisely, if the mean curvature vector at a point vanishes, then the equality case of this inequality is achieved by a unit tangent vector at the point if and only if the vector belongs to the normal space. Finally, we have shown that when a point is a totally geodesic point or is totally umbilical with n=2, the equality case of this inequality holds true for all unit tangent vectors at the point, and conversely.<\/jats:p>","DOI":"10.3390\/axioms13070454","type":"journal-article","created":{"date-parts":[[2024,7,4]],"date-time":"2024-07-04T06:28:54Z","timestamp":1720074534000},"page":"454","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":8,"title":["Analyzing the Ricci Tensor for Slant Submanifolds in Locally Metallic Product Space Forms with a Semi-Symmetric Metric Connection"],"prefix":"10.3390","volume":"13","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-1614-3228","authenticated-orcid":false,"given":"Yanlin","family":"Li","sequence":"first","affiliation":[{"name":"School of Mathematics, Hangzhou Normal University, Hangzhou 311121, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Md","family":"Aquib","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Statistics, College of Science, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh 11566, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6554-1228","authenticated-orcid":false,"given":"Meraj Ali","family":"Khan","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Statistics, College of Science, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh 11566, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5901-2511","authenticated-orcid":false,"given":"Ibrahim","family":"Al-Dayel","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Statistics, College of Science, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh 11566, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Khalid","family":"Masood","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Statistics, College of Science, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh 11566, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2024,7,4]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"154","DOI":"10.1007\/PL00000420","article-title":"On Ricci curvature of isotropic and Lagrangian submanifolds in complex space forms","volume":"74","author":"Chen","year":"2000","journal-title":"Arch. 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