{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,20]],"date-time":"2026-04-20T22:09:49Z","timestamp":1776722989630,"version":"3.51.2"},"reference-count":25,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2024,6,19]],"date-time":"2024-06-19T00:00:00Z","timestamp":1718755200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"the Deanship of Scientific Research at Imam Mohammad Ibn Saud Islamic University (IMSIU)","award":["IMSIU-RP23105"],"award-info":[{"award-number":["IMSIU-RP23105"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>Warped products provide an elegant and versatile framework for exploring and understanding a wide range of geometric structures. Their ability to combine two distinct manifolds through a warping function introduces a rich and diverse set of geometries, thus making them a powerful tool in various mathematical, physical, and computational applications. This article addresses the central query related to warped product submanifolds in the context of statistics. It focuses on deriving two new and distinct inequalities for a statistical warped product submanifold in a statistical manifold of a constant (quasi-constant) curvature. This article then finishes with some concluding remarks.<\/jats:p>","DOI":"10.3390\/sym16060771","type":"journal-article","created":{"date-parts":[[2024,6,20]],"date-time":"2024-06-20T05:27:19Z","timestamp":1718861239000},"page":"771","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Statistical Warped Product Immersions into Statistical Manifolds of (Quasi-)Constant Curvature"],"prefix":"10.3390","volume":"16","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-3895-7548","authenticated-orcid":false,"given":"Aliya Naaz","family":"Siddiqui","sequence":"first","affiliation":[{"name":"Division of Mathematics, School of Basic Sciences, Galgotias University, Greater Noida 203201, Uttar Pradesh, India"}],"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), P.O. Box 65892, Riyadh 11566, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Sudhakar Kumar","family":"Chaubey","sequence":"additional","affiliation":[{"name":"Department of Information Technology, University of Technology and Applied Sciences, P.O. Box 77, Shinas 324, Oman"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2024,6,19]]},"reference":[{"key":"ref_1","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":"1969","journal-title":"Trans. Am. Math. Soc."},{"key":"ref_2","first-page":"1","article-title":"Geometry of warped product submanifolds: A survey","volume":"6","author":"Chen","year":"2013","journal-title":"J. Adv. Math. Stud."},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Amari, S. (1985). Differential Geometric Methods in Statistics, Springer. 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