Biharmonic Lorentz hypersurfaces in E₁⁴

Andreas Arvanitoyeorgos, Filip Defever, George Kaimakamis and Vassilis J. Papantoniou

Vol. 229 (2007), No. 2, 293–305

DOI: 10.2140/pjm.2007.229.293

Abstract

A submanifold M_rⁿ of pseudo-Euclidean space E_s⁴ is said to have harmonic mean curvature vector if ΔH = 0, where H denotes the mean curvature vector field and Δ the Laplacian of the induced pseudo-Riemannian metric. We prove that every nondegenerate Lorentz hypersurface M₁³ of E₁⁴ with harmonic mean curvature vector is minimal.

Keywords

pseudo-Euclidean space, biharmonic hypersurface, minimal hypersurface

Mathematical Subject Classification 2000

Primary: 53A07, 53C40

Secondary: 53C50

Milestones

Received: 18 July 2005

Revised: 3 October 2005

Accepted: 3 October 2005

Published: 1 February 2007