{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,27]],"date-time":"2026-02-27T00:16:44Z","timestamp":1772151404152,"version":"3.50.1"},"reference-count":29,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2025,7,26]],"date-time":"2025-07-26T00:00:00Z","timestamp":1753488000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>The current work establishes the geometrical bearing for hypersurfaces in a Golden Riemannian manifold with constant golden sectional curvature with respect to k-almost Newton-conformal Ricci solitons. Moreover, we extensively explore the immersed r-almost Newton-conformal Ricci soliton and determine the sufficient conditions for total geodesicity with adequate restrictions on some smooth functions using mathematical operators. Furthermore, we go over some natural conclusions in which the gradient k-almost Newton-conformal Ricci soliton on the hypersurface of the Golden Riemannian manifold becomes compact. Finally, we establish a Schur\u2019s type inequality in terms of k-almost Newton-conformal Ricci solitons immersed in Golden Riemannian manifolds with constant golden sectional curvature.<\/jats:p>","DOI":"10.3390\/axioms14080579","type":"journal-article","created":{"date-parts":[[2025,7,28]],"date-time":"2025-07-28T09:53:02Z","timestamp":1753696382000},"page":"579","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["k-Almost Newton-Conformal Ricci Solitons on Hypersurfaces Within Golden Riemannian Manifolds with Constant Golden Sectional Curvature"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0009-0003-2258-991X","authenticated-orcid":false,"given":"Amit Kumar","family":"Rai","sequence":"first","affiliation":[{"name":"Department of Applied Sciences, GTBIT, GGSIPU, G-8 Area, Rajouri Garden, New Delhi 110064, India"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Majid Ali","family":"Choudhary","sequence":"additional","affiliation":[{"name":"Department of Mathematics, School of Sciences, Maulana Azad National Urdu University, Hyderabad 500032, India"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1713-6831","authenticated-orcid":false,"given":"Mohd. Danish","family":"Siddiqi","sequence":"additional","affiliation":[{"name":"Department of Mathematics, College of Science, Jazan University, P.O. Box 277, Jazan 45142, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ghodratallah","family":"Fasihi-Ramandi","sequence":"additional","affiliation":[{"name":"Department of Pure Mathematics, Faculty of Science, Imam Khomeini International University, Qazvin 34148-96818, Iran"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Uday Chand","family":"De","sequence":"additional","affiliation":[{"name":"Department of Pure Mathematics, University of Calcutta 35, Ballygunge Circular Road, Kolkata 700019, India"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3782-2983","authenticated-orcid":false,"given":"Ion","family":"Mihai","sequence":"additional","affiliation":[{"name":"Faculty of Mathematics and Computer Science, University of Bucharest, 010014 Bucharest, Romania"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2025,7,26]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"237","DOI":"10.1090\/conm\/071\/954419","article-title":"The Ricci flow on surfaces, Mathematics and general relativity (Santa Cruz. 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