{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,7]],"date-time":"2026-04-07T22:45:36Z","timestamp":1775601936609,"version":"3.50.1"},"reference-count":20,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T00:00:00Z","timestamp":1740096000000},"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":["Axioms"],"abstract":"<jats:p>A closed conformal vector field in de Sitter space S1n+1c\u00af induces a vector field on a spacelike hypersurface M of S1n+1c\u00af, referred to as the induced vector field on M. This article investigates the characterization of compact spacelike hypersurfaces in de Sitter space without assuming the constancy of the mean curvature. Specifically, we establish that under certain conditions, a compact spacelike hypersurface in S1n+1c\u00af is a sphere, that is, a totally umbilical hypersurface with constant mean curvature. We also present a different characterization of compact spacelike hypersurfaces in de Sitter space as spheres by using a lower bound on the integral of the Ricci curvature of the compact hypersurface in the direction of the induced vector field. We also consider de Sitter space as a Robertson\u2013Walker space and provide several characterizations of spheres within its spacelike hypersurfaces.<\/jats:p>","DOI":"10.3390\/axioms14030155","type":"journal-article","created":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T03:47:46Z","timestamp":1740109666000},"page":"155","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":8,"title":["Spacelike Hypersurfaces in de Sitter Space"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-1614-3228","authenticated-orcid":false,"given":"Yanlin","family":"Li","sequence":"first","affiliation":[{"name":"School of Mathematics, Hangzhou Normal University, Hangzhou 311121, China"}]},{"ORCID":"https:\/\/orcid.org\/0009-0001-4088-6606","authenticated-orcid":false,"given":"Mona","family":"Bin-Asfour","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Statistics, College of Science, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh 13318, Saudi Arabia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1204-8568","authenticated-orcid":false,"given":"Kholoud Saad","family":"Albalawi","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Statistics, College of Science, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh 13318, Saudi Arabia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0775-2323","authenticated-orcid":false,"given":"Mohammed","family":"Guediri","sequence":"additional","affiliation":[{"name":"Department of Mathematics, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia"}]}],"member":"1968","published-online":{"date-parts":[[2025,2,21]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Alessa, N., and Guediri, M. (2023). Generalized Minkowski type integral formulas for compact hypersurfaces in pseudo-Riemannian manifolds. Mathematics, 11.","DOI":"10.20944\/preprints202309.0043.v1"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"13","DOI":"10.1007\/BF01179263","article-title":"On Spacelike hypersurfaces with Constant Mean Curvature in the de Sitter Space","volume":"196","author":"Akutagawa","year":"1987","journal-title":"Math. Z."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"205","DOI":"10.3836\/tjm\/1270130500","article-title":"On spacelike hypersurfaces with constant mean curvature of a Lorentz space form","volume":"14","author":"Ki","year":"1991","journal-title":"Tokyo J. 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On spacelike hypersurfaces in generalized Robertson\u2013Walker spacetimes. Axioms, 13.","DOI":"10.3390\/axioms13090636"}],"container-title":["Axioms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2075-1680\/14\/3\/155\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,9]],"date-time":"2025-10-09T16:39:16Z","timestamp":1760027956000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2075-1680\/14\/3\/155"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,2,21]]},"references-count":20,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2025,3]]}},"alternative-id":["axioms14030155"],"URL":"https:\/\/doi.org\/10.3390\/axioms14030155","relation":{},"ISSN":["2075-1680"],"issn-type":[{"value":"2075-1680","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,2,21]]}}}