{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,3]],"date-time":"2026-06-03T03:14:51Z","timestamp":1780456491403,"version":"3.54.1"},"reference-count":30,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2025,3,22]],"date-time":"2025-03-22T00:00:00Z","timestamp":1742601600000},"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>We investigate f-biharmonic submanifolds in T-space form, where we analyze different scenarios and provide necessary and sufficient conditions for f-biharmonicity. We also derive a non-existence result for f-biharmonic submanifolds where \u03be and \u03d5\u03a9 are tangents. Finally, we derive the Chen\u2013Ricci inequality for submanifolds of T-space forms and provide the conditions under which this inequality becomes equality.<\/jats:p>","DOI":"10.3390\/axioms14040242","type":"journal-article","created":{"date-parts":[[2025,3,24]],"date-time":"2025-03-24T06:21:38Z","timestamp":1742797298000},"page":"242","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Classification Results of f-Biharmonic Immersion in T-Space Forms"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-9343-0725","authenticated-orcid":false,"given":"Md","family":"Aquib","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"}]},{"given":"Mohd","family":"Iqbal","sequence":"additional","affiliation":[{"name":"Department of Mathematics, ARSD College, South Campus, University of Delhi, Delhi 110021, India"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6908-6146","authenticated-orcid":false,"given":"Sarvesh Kumar","family":"Yadav","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Natural Sciences, Jamia Millia Islamia, New Delhi 110025, India"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2025,3,22]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"385","DOI":"10.1112\/blms\/20.5.385","article-title":"Report on harmonic maps","volume":"20","author":"Eells","year":"1988","journal-title":"Bull. Lond. Math. 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