{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,8]],"date-time":"2026-01-08T20:07:12Z","timestamp":1767902832446,"version":"3.49.0"},"reference-count":28,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2026,1,8]],"date-time":"2026-01-08T00:00:00Z","timestamp":1767830400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Princess Nourah bint Abdulrahman University, Riyadh, Saudi Arabia","award":["PNURSP2026R27"],"award-info":[{"award-number":["PNURSP2026R27"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>In this paper, we analyze a silver Riemannian structure on a Riemannian manifold. We compute some fundamental properties of the induced structure on submanifolds immersed in a silver Riemannian manifold and also obtain some results for induced structures on submanifolds of codimension 2. Moreover, we explore the conditions for totally geodesic and minimal submanifolds in a silver Riemannian manifold. Finally, we also give an example of submanifolds in a silver Riemannian manifold.<\/jats:p>","DOI":"10.3390\/axioms15010047","type":"journal-article","created":{"date-parts":[[2026,1,8]],"date-time":"2026-01-08T15:33:16Z","timestamp":1767886396000},"page":"47","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Geometrical Analysis on Submanifolds in Riemannian Manifolds Attached with Silver Structure"],"prefix":"10.3390","volume":"15","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-0252-9672","authenticated-orcid":false,"given":"Shadab Ahmad","family":"Khan","sequence":"first","affiliation":[{"name":"Department of Mathematics & Statistics, Integral University, Lucknow 226026, India"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2116-7382","authenticated-orcid":false,"given":"Fatemah","family":"Mofarreh","sequence":"additional","affiliation":[{"name":"Mathematical Science Department, Faculty of Science, Princess Nourah bint Abdulrahman University, Riyadh 11546, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1176-4666","authenticated-orcid":false,"given":"Toukeer","family":"Khan","sequence":"additional","affiliation":[{"name":"Department of Liberal Education, Era University, Lucknow 226003, 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":"Anis","family":"Ahmad","sequence":"additional","affiliation":[{"name":"Department of Mathematics & Statistics, Integral University, Lucknow 226026, India"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2026,1,8]]},"reference":[{"key":"ref_1","first-page":"83","article-title":"Submanifolds in metallic Riemannian manifolds","volume":"20","author":"Hretcanu","year":"2018","journal-title":"Differ. Geom. Dyn. Syst."},{"key":"ref_2","first-page":"279","article-title":"The metallic means family and forbidden symmetric","volume":"2","year":"2002","journal-title":"Int. Math. J."},{"key":"ref_3","first-page":"287","article-title":"On F2\u03f5-planar mappings of (pseudo-) Riemannian manifolds","volume":"50","author":"Hinterleitner","year":"2014","journal-title":"Arch. 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