{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T00:36:13Z","timestamp":1760142973502,"version":"build-2065373602"},"reference-count":32,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2024,1,11]],"date-time":"2024-01-11T00:00:00Z","timestamp":1704931200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100002713","name":"Imam Mohammad ibn Saud Islamic University","doi-asserted-by":"publisher","award":["IMSIU-RP23078"],"award-info":[{"award-number":["IMSIU-RP23078"]}],"id":[{"id":"10.13039\/501100002713","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>The primary objective of this paper is to explore contact CR-warped product submanifolds of Sasakian space forms equipped with a semi-symmetric metric connection. We thoroughly examine these submanifolds and establish various key findings. Furthermore, we derive an inequality relating the Ricci curvature to the mean curvature vector and warping function.<\/jats:p>","DOI":"10.3390\/sym16010095","type":"journal-article","created":{"date-parts":[[2024,1,11]],"date-time":"2024-01-11T12:56:33Z","timestamp":1704977793000},"page":"95","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Ricci Curvature Inequalities for Contact CR-Warped Product Submanifolds of an Odd Dimensional Sphere Admitting a 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"}],"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), P.O. Box 65892, Riyadh 11566, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0009-0003-7359-484X","authenticated-orcid":false,"given":"Foued","family":"Aloui","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"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2024,1,11]]},"reference":[{"key":"ref_1","unstructured":"Beem, J.K., Ehrlich, P., and Powell, T.G. (1982). Warped Product Manifolds in Relativity Selected Studies, North-Holland."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"333","DOI":"10.2969\/jmsj\/01430333","article-title":"Certain conditions for a Riemannian manifold to be isometric with a sphere","volume":"14","author":"Obata","year":"1962","journal-title":"J. Math. Soc. JPN"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1090\/S0002-9947-1969-0251664-4","article-title":"Manifolds of Negative curvature","volume":"145","author":"Bishop","year":"1965","journal-title":"Trans. Am. Math. Soc."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"177","DOI":"10.1007\/s006050170019","article-title":"Geometry of warped product CR-submanifolds in Kaehler manifolds I","volume":"133","author":"Chen","year":"2001","journal-title":"Monatsh Math."},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Chen, B.Y. (2017). Differential Geometry of Warped Product Manifolds and Submanifolds, World Scientific Publishing Company.","DOI":"10.1142\/10419"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"143","DOI":"10.1023\/B:GEOM.0000006582.29685.22","article-title":"Contact CR-warped product submanifolds in Sasakian manifolds","volume":"102","author":"Hasegawa","year":"2003","journal-title":"Geom. Dedicata"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"165","DOI":"10.1007\/s10711-004-5459-z","article-title":"Contact CR-warped product submanifolds in Sasakian space forms","volume":"109","author":"Mihai","year":"2004","journal-title":"Geom. Dedicata"},{"key":"ref_8","first-page":"143","article-title":"Geometry of warped product submanifolds a survey","volume":"6","author":"Chen","year":"2013","journal-title":"J. Adv. Math. Stud."},{"key":"ref_9","first-page":"41","article-title":"Relations between Ricci curvature and shape operator for submanifolds with arbitrary codimension","volume":"33","author":"Chen","year":"1999","journal-title":"Glasgow Math. J."},{"key":"ref_10","first-page":"1465","article-title":"Chen inequalities for submanifolds of real space forms with a semi-symmetric metric connection, Taiwan","volume":"14","author":"Mihai","year":"2010","journal-title":"J. Math."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"322","DOI":"10.1080\/16583655.2020.1738704","article-title":"Chen optimal inequalities of CR-warped products of generalized Sasakian space forms","volume":"14","author":"Siddiqui","year":"2020","journal-title":"J. Taibah Univ. Sci."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"1731","DOI":"10.1155\/S016117120311215X","article-title":"Inequalities for semislant submanifolds in Sasakian space forms","volume":"27","author":"Cioroboiu","year":"2003","journal-title":"Int. J. Math. Math. Sci."},{"key":"ref_13","first-page":"43","article-title":"Inequality for Ricci curvature of slant submanifolds in cosymplectic space forms","volume":"30","author":"Yoon","year":"2006","journal-title":"Turk. J. Math."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"247","DOI":"10.1017\/S1446788700003888","article-title":"Ricci curvature of submanifolds in Sasakian space forms","volume":"72","author":"Mihai","year":"2002","journal-title":"J. Aust. Math. Soc."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"30","DOI":"10.1016\/j.difgeo.2018.12.006","article-title":"Classification of Casorati ideal Lagrangian submanifolds in complex space forms","volume":"63","author":"Aquib","year":"2019","journal-title":"Differ. Geom. Appl."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"103510","DOI":"10.1016\/j.geomphys.2019.103510","article-title":"Ricci curvature on warped product submanifolds in spheres with geometric applications","volume":"146","author":"Ali","year":"2019","journal-title":"J. Geom. Phys."},{"key":"ref_17","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_18","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":"Proc. Lond. Math. Soc. II Ser."},{"key":"ref_19","first-page":"1579","article-title":"On semi-symmetric metric connections","volume":"15","author":"Yano","year":"1970","journal-title":"Rev. Roumaine Math. Pures Appl."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"1701","DOI":"10.11650\/twjm\/1500406374","article-title":"Warped products with a semi-symmetric metric connection","volume":"15","author":"Sular","year":"2011","journal-title":"Taiwan J. Math."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"461","DOI":"10.1007\/s13369-011-0045-9","article-title":"Warped Products with a Semi-Symmetric Non-Metric Connection","volume":"36","author":"Sular","year":"2011","journal-title":"Arab. J. Sci. Eng."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"1950118","DOI":"10.1142\/S0219887819501184","article-title":"Chen inequalities for submanifolds of complex space forms and Sasakian space forms with quarter symmetric connections","volume":"16","author":"Wang","year":"2019","journal-title":"Int. J. Geom. Methods Mod. Phys."},{"key":"ref_23","first-page":"135","article-title":"CR submanifolds of a Kaehler manifold I","volume":"69","author":"Bejancu","year":"1978","journal-title":"Proc. Am. Math. Soc."},{"key":"ref_24","doi-asserted-by":"crossref","unstructured":"Li, Y., Gupta, M.K., Sharma, S., and Chaubey, S.K. (2023). On Ricci Curvature of a Homogeneous Generalized Matsumoto Finsler Space. Mathematics, 11.","DOI":"10.3390\/math11153365"},{"key":"ref_25","doi-asserted-by":"crossref","unstructured":"Li, Y., and G\u00fcler, E. (2023). A Hypersurfaces of Revolution Family in the Five-Dimensional Pseudo-Euclidean Space E25. Mathematics, 11.","DOI":"10.3390\/math11153427"},{"key":"ref_26","doi-asserted-by":"crossref","unstructured":"Li, Y., and Mak, M. (2023). Framed Natural Mates of Framed Curves in Euclidean 3-Space. Mathematics, 11.","DOI":"10.3390\/math11163571"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"20220610","DOI":"10.1515\/math-2022-0610","article-title":"Geometric classifications of k-almost Ricci solitons admitting paracontact metrices","volume":"21","author":"Li","year":"2023","journal-title":"Open Math."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"24957","DOI":"10.3934\/math.20231273","article-title":"Hypersurfaces of revolution family supplying in pseudo-Euclidean space","volume":"8","author":"Li","year":"2023","journal-title":"AIMS Math."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"20220252","DOI":"10.1515\/dema-2022-0252","article-title":"Kinematic-geometry of a line trajectory and the invariants of the axodes","volume":"56","author":"Li","year":"2023","journal-title":"Demonstratio Math."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"1","DOI":"10.2298\/FIL2404423L","article-title":"On the Curvatures of Timelike Circular Surfaces in Lorentz-Minkowski Space","volume":"38","author":"Li","year":"2024","journal-title":"Filomat"},{"key":"ref_31","doi-asserted-by":"crossref","unstructured":"Li, Y., and G\u00fcler, E. (2023). Twisted Hypersurfaces in Euclidean 5-Space. Mathematics, 11.","DOI":"10.3390\/math11224612"},{"key":"ref_32","doi-asserted-by":"crossref","unstructured":"Li, Y., Mofarreh, F., Abolarinwa, A., Alshehri, N., and Ali, A. (2023). Bounds for Eigenvalues of q-Laplacian on Contact Submanifolds of Sasakian Space Forms. Mathematics, 11.","DOI":"10.3390\/math11234717"}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/16\/1\/95\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T13:44:58Z","timestamp":1760103898000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/16\/1\/95"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,1,11]]},"references-count":32,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2024,1]]}},"alternative-id":["sym16010095"],"URL":"https:\/\/doi.org\/10.3390\/sym16010095","relation":{},"ISSN":["2073-8994"],"issn-type":[{"type":"electronic","value":"2073-8994"}],"subject":[],"published":{"date-parts":[[2024,1,11]]}}}