Classification Results of <i>f</i>-Biharmonic Immersion in <i>T</i>-Space Forms
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 <inline-formula><math xmlns="http://www.w3.org/1...
| Published in: | Axioms |
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| Main Authors: | , , |
| Format: | Article |
| Language: | English |
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MDPI AG
2025-03-01
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| Online Access: | https://www.mdpi.com/2075-1680/14/4/242 |
| _version_ | 1849672506530594816 |
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| author | Md Aquib Mohd Iqbal Sarvesh Kumar Yadav |
| author_facet | Md Aquib Mohd Iqbal Sarvesh Kumar Yadav |
| author_sort | Md Aquib |
| collection | DOAJ |
| container_title | Axioms |
| description | 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 <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>ξ</mi></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>ϕ</mi><mo>Ω</mo></mrow></semantics></math></inline-formula> are tangents. Finally, we derive the Chen–Ricci inequality for submanifolds of <i>T</i>-space forms and provide the conditions under which this inequality becomes equality. |
| format | Article |
| id | doaj-art-feffdd7d1892421fa17e87f62107daef |
| institution | Directory of Open Access Journals |
| issn | 2075-1680 |
| language | English |
| publishDate | 2025-03-01 |
| publisher | MDPI AG |
| record_format | Article |
| spelling | doaj-art-feffdd7d1892421fa17e87f62107daef2025-08-20T02:17:14ZengMDPI AGAxioms2075-16802025-03-0114424210.3390/axioms14040242Classification Results of <i>f</i>-Biharmonic Immersion in <i>T</i>-Space FormsMd Aquib0Mohd Iqbal1Sarvesh Kumar Yadav2Department of Mathematics and Statistics, College of Science, Imam Mohammad Ibn Saud Islamic University (IMSIU), P.O. Box 65892, Riyadh 11566, Saudi ArabiaDepartment of Mathematics, ARSD College, South Campus, University of Delhi, Delhi 110021, IndiaDepartment of Mathematics, Faculty of Natural Sciences, Jamia Millia Islamia, New Delhi 110025, IndiaWe 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 <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>ξ</mi></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>ϕ</mi><mo>Ω</mo></mrow></semantics></math></inline-formula> are tangents. Finally, we derive the Chen–Ricci inequality for submanifolds of <i>T</i>-space forms and provide the conditions under which this inequality becomes equality.https://www.mdpi.com/2075-1680/14/4/242Chen–Ricci inequalityf-biharmonic submanifoldsT-space forms |
| spellingShingle | Md Aquib Mohd Iqbal Sarvesh Kumar Yadav Classification Results of <i>f</i>-Biharmonic Immersion in <i>T</i>-Space Forms Chen–Ricci inequality f-biharmonic submanifolds T-space forms |
| title | Classification Results of <i>f</i>-Biharmonic Immersion in <i>T</i>-Space Forms |
| title_full | Classification Results of <i>f</i>-Biharmonic Immersion in <i>T</i>-Space Forms |
| title_fullStr | Classification Results of <i>f</i>-Biharmonic Immersion in <i>T</i>-Space Forms |
| title_full_unstemmed | Classification Results of <i>f</i>-Biharmonic Immersion in <i>T</i>-Space Forms |
| title_short | Classification Results of <i>f</i>-Biharmonic Immersion in <i>T</i>-Space Forms |
| title_sort | classification results of i f i biharmonic immersion in i t i space forms |
| topic | Chen–Ricci inequality f-biharmonic submanifolds T-space forms |
| url | https://www.mdpi.com/2075-1680/14/4/242 |
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