Biconservative hypersurfaces in Euclidean Spaces

Abstract

An isometric immersion $X: Σ^n \longrightarrow \mathbb{E}^{n+1}$ is biharmonic (BHH) if $Δ^2 X = 0$, i.e., if $ΔH =0$, where $Δ$ and $H$ are the metric Laplacian and the mean curvature vector field of $Σ^n$ respectively. More generally, biconservative hypersurfaces (BCHs) are isometric immersions for which only the tangential part of the biharmonic equation vanishes. BCHs are first described and then constructed.