Biharmonic submanifolds of generalized space forms

TL;DR

This paper investigates biharmonic submanifolds within generalized complex and Sasakian space forms, deriving conditions and curvature estimates for various submanifold types.

Contribution

It provides new biharmonicity conditions and curvature bounds for submanifolds in generalized complex and Sasakian space forms, covering multiple specific cases.

Findings

Derived biharmonicity conditions for submanifolds.

Obtained curvature estimates for particular submanifold classes.

Analyzed curves, surfaces, and hypersurfaces in these spaces.

Abstract

We consider biharmonic submanifolds in both generalized complex and Sasakian space forms. After giving the biharmonicity conditions for submanifolds in these spaces, we study different particular cases for which we obtain curvature estimates. We consider curves, complex and Lagrangian surfaces and hypersurfaces for the generalized complex space form as well as hypersurfaces, invariant and anti-invariant submanifolds in case of generalized Sasakian space form.