f-Biharmonic and bi-f-harmonic submanifolds of generalized space forms

TL;DR

This paper investigates the properties of f-biharmonic and bi-f-harmonic submanifolds within generalized complex and Sasakian space forms, providing conditions for their existence and non-existence.

Contribution

It establishes necessary and sufficient conditions for f-biharmonic and bi-f-harmonic submanifolds in these geometric contexts, including specific cases and non-existence results.

Findings

Derived conditions for f-biharmonicity and bi-f-harmonicity

Identified cases with non-existence of such submanifolds

Extended understanding of harmonic submanifold theory in complex and Sasakian spaces

Abstract

We study f-biharmonic and bi-f-harmonic submanifolds in both generalized complex and Sasakian space forms. We prove necessary and sufficient condition for f-biharmonicity and bi-f-harmonicity in the general case and many particular cases. Some non-existence results are also obtained.