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