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First, we analyze the properties of these vector fields on Riemannian manifolds. Next, we focus on Ricci solitons on Riemannian hypersurfaces induced by torse-forming vector fields of Riemannian or Lorentzian manifolds. Specifically, we show that such a hypersurface in the manifold with constant sectional curvature is either totally geodesic or an extrinsic sphere.<\/jats:p>","DOI":"10.3390\/axioms14050325","type":"journal-article","created":{"date-parts":[[2025,4,23]],"date-time":"2025-04-23T06:38:37Z","timestamp":1745390317000},"page":"325","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Ricci Solitons on Riemannian Hypersurfaces Generated by Torse-Forming Vector Fields in Riemannian and Lorentzian Manifolds"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0009-0009-0392-3568","authenticated-orcid":false,"given":"Norah","family":"Alshehri","sequence":"first","affiliation":[{"name":"Department of Mathematics, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, 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":[[2025,4,23]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"36","DOI":"10.1007\/s10714-020-02690-2","article-title":"Cosmological perfect fluids in higher-order gravity","volume":"52","author":"Capozziello","year":"2020","journal-title":"Gen. Relativ. Gravit."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"1833","DOI":"10.1007\/s10714-014-1833-9","article-title":"A simple characterization of generalized Robertson-Walker spacetimes","volume":"46","author":"Chen","year":"2014","journal-title":"Gen. Relativ. 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