{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,4]],"date-time":"2026-06-04T19:59:44Z","timestamp":1780603184535,"version":"3.54.1"},"reference-count":26,"publisher":"MDPI AG","issue":"5","license":[{"start":{"date-parts":[[2025,4,25]],"date-time":"2025-04-25T00:00:00Z","timestamp":1745539200000},"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>In this paper, we introduce the concept of contravariant Einstein-like Poisson manifolds of classes A, B, and P. We then prove that the fiber space of a Poisson warped product manifold inherits the contravariant Einstein-like classes of the total space, while the base space inherits these classes under certain conditions related to the warping function. We also explore applications of contravariant Einstein-like Poisson structures in various spacetime models, including generalized Robertson\u2013Walker, Reissner\u2013Nordstr\u00f6m, and standard static spacetimes.<\/jats:p>","DOI":"10.3390\/sym17050645","type":"journal-article","created":{"date-parts":[[2025,4,25]],"date-time":"2025-04-25T06:10:13Z","timestamp":1745561413000},"page":"645","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Einstein-like Poisson Warped Product Manifolds and Applications"],"prefix":"10.3390","volume":"17","author":[{"ORCID":"https:\/\/orcid.org\/0009-0003-7359-484X","authenticated-orcid":false,"given":"Foued","family":"Aloui","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":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2025,4,25]]},"reference":[{"key":"ref_1","first-page":"266","article-title":"M\u00e9moire sur la variation des constantes arbitraires dans les questions de m\u00e9canique","volume":"8","author":"Poisson","year":"1809","journal-title":"J. \u00c9c. Polytech."},{"key":"ref_2","first-page":"253","article-title":"Les vari\u00e9t\u00e9s de Poisson et leurs alg\u00e8bres de Lie associ\u00e9es","volume":"12","author":"Lichnerowicz","year":"1977","journal-title":"J. Diff. Geom."},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Vaisman, I. (1994). Lectures on the Geometry of Poisson Manifolds, Birkh\u00e4user. Progress in Mathematics.","DOI":"10.1007\/978-3-0348-8495-2"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"303","DOI":"10.4310\/jdg\/1214341648","article-title":"Connections in Poisson geometry I. 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