Geodesic
A short note on $f$-biharmonic hypersurfaces
Commentationes Mathematicae Universitatis Carolinae, Tome 61 (2020) no. 1, pp. 119-126.

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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 $S^{2}\times \mathbb{R}$.
DOI : 10.14712/1213-7243.2020.009
Classification : 53C25, 53C43, 58E20
Keywords: $f$-biharmonic maps; $f$-biharmonic hypersurface 
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Perktaş, Selcen Y.; Acet, Bilal E.; Blaga, Adara M. A short note on $f$-biharmonic hypersurfaces. Commentationes Mathematicae Universitatis Carolinae, Tome 61 (2020) no. 1, pp. 119-126. doi : 10.14712/1213-7243.2020.009. http://geodesic.mathdoc.fr/articles/10.14712/1213-7243.2020.009/

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