Biharmonic Hypersurfaces in Euclidean Spaces

Hiba Bibi, Marc Soret, Marina Ville

An isometric immersion $X:{\Sigma }^n⟶{\mathbb{E}}^{n+1}$ is biharmonic if ${\Delta }^{2}X=0$, i.e. if $\Delta H=0$, where $\Delta$ and $H$ are the metric Laplacian and the mean curvature ve…