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arXiv · 1204.5550

Biharmonic hypersurfaces in a conformally flat space

Liang Tang·Ye-Lin Ou
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Abstract

Biharmonic hypersurfaces in a generic conformally flat space are studied in this paper. The equation of such hypersurfaces is derived and is used to determine the conformally flat metric $f^{-2}δ_{ij}$ on the Euclidean space $\mathbb{R}^{m+1}$ so that a minimal hypersurface $M^m\longrightarrow (\mathbb{R}^{m+1}, δ_{ij})$ in a Euclidean space becomes a biharmonic hypersurface $M^m\longrightarrow (\mathbb{R}^{m+1}, f^{-2}δ_{ij})$ in the conformally flat space. Our examples include all biharmonic hypersurfaces found in [Ou1] and [OT] as special cases.

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Liang Tang, Ye-Lin Ou. 2012-04-25. Biharmonic hypersurfaces in a conformally flat space. https://arxiv.org/abs/1204.5550

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