Biconservative hypersurfaces in Euclidean Spaces

Hiba Bibi; Marc Soret; Marina Ville

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arXiv · 2610.16434

Biconservative hypersurfaces in Euclidean Spaces

Hiba Bibi·Marc Soret·Marina Ville

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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.

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BibTeX RIS

Hiba Bibi, Marc Soret, Marina Ville. 2026-10-12. Biconservative hypersurfaces in Euclidean Spaces. https://arxiv.org/abs/2610.16434

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