## Selcen Y. Perktaş, B\. ilal E. Acet, Adara M. Blaga

*A short note on $f$-biharmonic hypersurfaces*

Comment.Math.Univ.Carolin. 61,1 (2020) 119-126.**Abstract:**In the present paper we give some properties of $f$-biharmonic hypersurfaces in real space forms. By using the $f$-biharmonic equation for a hypersurface of a Riemannian manifold, we characterize the $f$-biharmonicity of constant mean curvature and totally umbilical hypersurfaces in a Riemannian manifold and, in particular, in a real space form. As an example, we consider $f$-biharmonic vertical cylinders in $S^{2}\times \mathbb{R}$.

**Keywords:** $f$-biharmonic maps; $f$-biharmonic hypersurface

**DOI:** DOI 10.14712/1213-7243.2020.009

**AMS Subject Classification:** 58E20 53C25 53C43

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