Remarks on biharmonic hypersurfaces in space forms

TL;DR

This paper investigates the properties of biharmonic hypersurfaces in space forms, establishing rigidity results and integral formulas that deepen understanding of their geometric structure.

Contribution

It provides new rigidity conditions for biharmonic hypersurfaces and derives integral formulas involving the position vector in space forms.

Findings

Rigidity result for closed biharmonic hypersurfaces in the Euclidean sphere.

An integral formula involving the position vector for biharmonic hypersurfaces in space forms.

Conditions on scalar curvature that influence biharmonic hypersurface properties.

Abstract

We consider closed biharmonic hypersurfaces in the Euclidean sphere and prove a rigidity result under a suitable condition on the scalar curvature. Moreover, we establish an integral formula involving the position vector for biharmonic hypersurfaces in space forms.