{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T01:34:23Z","timestamp":1760146463569,"version":"build-2065373602"},"reference-count":31,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2024,11,4]],"date-time":"2024-11-04T00:00:00Z","timestamp":1730678400000},"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-RP23036"],"award-info":[{"award-number":["IMSIU-RP23036"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>In this paper, we explore the uses of Obata\u2019s differential equation in relation to the Ricci curvature of an odd-dimensional sphere that possesses a semi-symmetric metric connection. Specifically, we establish that, given certain conditions, the underlying submanifold can be identified as an isometric sphere. Additionally, we investigate the impact of specific differential equations on these submanifolds and demonstrate that, when certain geometric conditions are met, the base submanifold can be characterized as a special type of warped product.<\/jats:p>","DOI":"10.3390\/sym16111463","type":"journal-article","created":{"date-parts":[[2024,11,4]],"date-time":"2024-11-04T05:41:23Z","timestamp":1730698883000},"page":"1463","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Application of Differential Equations on the Ricci Curvature of Contact CR-Warped Product Submanifolds of S2n+1(1) with Semi-Symmetric Metric Connection"],"prefix":"10.3390","volume":"16","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-6554-1228","authenticated-orcid":false,"given":"Meraj Ali","family":"Khan","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"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1729-4805","authenticated-orcid":false,"given":"Amira A.","family":"Ishan","sequence":"additional","affiliation":[{"name":"Department of Mathematics, College of Science, Taif University, Taif 21944, Saudi Arabia"}]},{"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"}]},{"given":"Khalid","family":"Masood","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"}]}],"member":"1968","published-online":{"date-parts":[[2024,11,4]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"27","DOI":"10.1112\/plms\/s2-34.1.27","article-title":"Subspace of a space with torsion","volume":"34","author":"Hayden","year":"1932","journal-title":"J. Lond. Math. Soc."},{"key":"ref_2","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. Z."},{"key":"ref_3","first-page":"1579","article-title":"On semi-symmetric metric connections","volume":"15","author":"Yano","year":"1970","journal-title":"Rev. Roum. Math. 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