Biharmonic hypersurfaces in a conformally flat space

2012/04/25 by Liang Tang, Tang, Liang, Ye‐Lin Ou +1
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.1204.5550

openalex publication_date 2012/04/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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^-2δ_ij on the Euclidean space ℝ^m+1 so that a minimal hypersurface M^m\longrightarrow (ℝ^m+1, δ_ij) in a Euclidean space becomes a biharmonic hypersurface M^m\longrightarrow (ℝ^m+1, f^-2δ_ij) in the conformally flat space. Our examples include all biharmonic hypersurfaces found in [Ou1] and [OT] as special cases.

Citations

• Classifications and Isolation Phenomena of Bi-Harmonic Maps and Bi-Yang-Mills Fields
• Biharmonic submanifolds with parallel mean curvature in\n mathbbSⁿ\×\ℝ

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