{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T02:45:49Z","timestamp":1760150749728,"version":"build-2065373602"},"reference-count":39,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2023,12,28]],"date-time":"2023-12-28T00:00:00Z","timestamp":1703721600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>The purpose of this paper is to investigate a warped product of hemi-slant submanifolds on an S-manifold. We prove many interesting results for the existence of warped product hemi-slant submanifold of the type M\u03b8\u00d7fM\u22a5 with \u03be\u03b1\u2208M\u03b8 of an S-manifold. For such submanifolds, a characterization theorem is proven. In addition, we form an inequality for the squared norm of the second fundamental form in terms of the warping function and the slant angle. We also provide some examples, and the equality case is also considered.<\/jats:p>","DOI":"10.3390\/sym16010035","type":"journal-article","created":{"date-parts":[[2023,12,28]],"date-time":"2023-12-28T03:30:34Z","timestamp":1703734234000},"page":"35","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Geometry of Warped Product Hemi-Slant Submanifolds of an S-Manifold"],"prefix":"10.3390","volume":"16","author":[{"ORCID":"https:\/\/orcid.org\/0009-0003-0483-1426","authenticated-orcid":false,"given":"Ahlam","family":"Al-Mutairi","sequence":"first","affiliation":[{"name":"Department of Mathematics and Statistics, Faculty of Science, University of Jeddah, Jeddah 23890, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0009-0009-4360-3091","authenticated-orcid":false,"given":"Reem","family":"Al-Ghefari","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Statistics, Faculty of Science, University of Jeddah, Jeddah 23890, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5560-2944","authenticated-orcid":false,"given":"Awatif","family":"Al-Jedani","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Statistics, Faculty of Science, University of Jeddah, Jeddah 23890, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2023,12,28]]},"reference":[{"key":"ref_1","first-page":"99","article-title":"On a structure defined by a tensor field f of type (1,1) satisfying f3 + f = 0","volume":"14","author":"Yano","year":"1963","journal-title":"Tensor"},{"key":"ref_2","first-page":"456","article-title":"Globally framed f-manifold III","volume":"15","author":"Oldberg","year":"1971","journal-title":"J. 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