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Biconservative hypersurfaces in Euclidean Spaces
Abstract
An isometric immersion X: Σn ⟶ 𝔼n+1 is biharmonic (BHH) if Δ2 X = 0, i.e., if ΔH =0, where Δ and H are the metric Laplacian and the mean curvature vector field of Σn 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.
Related
- Biconservative and Biharmonic Hypersurfaces in Product Spaces
- Biconservative hypersurfaces in space forms with harmonic curvature
- Rigidity of Euclidean Minimal Hypersurfaces under Nonuniform Diagonal Dilations
- Generalised Killing Spinors and Euclidean Hypersurfaces
- Locally symmetric hypersurfaces in globally symmetric spaces
BibTeX
@misc{bibi2026biconservative,
title = {{Biconservative hypersurfaces in Euclidean Spaces}},
author = {Hiba Bibi and Marc Soret and Marina Ville},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.16434},
eprint = {2610.16434},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.16434},
}
RIS
TY - UNPB
TI - Biconservative hypersurfaces in Euclidean Spaces
AU - Hiba Bibi
AU - Marc Soret
AU - Marina Ville
PY - 2026
DA - 2026/10/12
PB - arXiv
DO - 10.48550/arxiv.2610.16434
UR - https://arxiv.org/abs/2610.16434
AB - An isometric immersion X: Σ^n ⟶ 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.
ER -