Classification Results of f-Biharmonic Immersion in T-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 ξ and ϕΩ are tangents. Finally, we derive the Chen–Ricci inequality for submanifolds of T-space forms and provide the conditions under which this inequality becomes equality.