{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T00:53:16Z","timestamp":1760057596604,"version":"build-2065373602"},"reference-count":39,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2025,2,11]],"date-time":"2025-02-11T00:00:00Z","timestamp":1739232000000},"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-DDRSP2502"],"award-info":[{"award-number":["IMSIU-DDRSP2502"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>This study is focused on pioneering new upper bounds on mean curvature and constant sectional curvature relative to the first positive eigenvalue of the generalized Laplacian operator in the differentiable manifolds with a semi-symmetric metric connection. Multiple approaches are being explored to determine the principal eigenvalue for the generalized-Laplacian operator in closed oriented-slant submanifolds within a Sasakian space form (ssf) with a semi-symmetric metric (ssm) connection. By utilizing our findings on the Laplacian, we extend several Reilly-type inequalities to the generalized Laplacian on slant submanifolds within a unit sphere with a semi-symmetric metric (ssm) connection. The research is concluded with a detailed examination of specific scenarios.<\/jats:p>","DOI":"10.3390\/sym17020279","type":"journal-article","created":{"date-parts":[[2025,2,11]],"date-time":"2025-02-11T11:01:08Z","timestamp":1739271668000},"page":"279","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Eigenvalues for the Generalized Laplace Operator of Slant Submanifolds in the Sasakian Space Forms Admitting Semi-Symmetric Metric Connection"],"prefix":"10.3390","volume":"17","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-5901-2511","authenticated-orcid":false,"given":"Ibrahim","family":"Al-Dayel","sequence":"first","affiliation":[{"name":"Department of Mathematics and Statistics, College of Science, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh 11566, Saudi Arabia"}]},{"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"}]},{"given":"Sudhakar Kumar","family":"Chaubey","sequence":"additional","affiliation":[{"name":"Section of Mathematics, Department of Information Technology, College of Computing and Information Sciences, University of Technology and Applied Sciences-Shinas, Shinas 324, Oman"}]}],"member":"1968","published-online":{"date-parts":[[2025,2,11]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"211","DOI":"10.1007\/BF01187468","article-title":"\u00dcber die Geometrie der halbsymmetrischen \u00dcbertragungen","volume":"21","author":"Friedmann","year":"1924","journal-title":"Math. 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