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Annals of Global Analysis and Geometry

, Volume 34, Issue 4, pp 403–414 | Cite as

Conformal and semi-conformal biharmonic maps

  • Paul Baird
  • Ali Fardoun
  • Seddik Ouakkas
Original Paper

Abstract

We show that a conformal mapping between Riemannian manifolds of the same dimension n ≥ 3 is biharmonic if and only if the gradient of its dilation satisfies a certain second-order elliptic partial differential equation. On an Einstein manifold solutions can be generated from isoparametric functions. We characterise those semi-conformal submersions that are biharmonic in terms of their dilation and the fibre mean curvature vector field.

Keywords

Conformal map Semi-conformal map Biharmonic map 

Mathematics Subject Classification (2000)

31B30 53A30 

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Copyright information

© Springer Science+Business Media B.V. 2008

Authors and Affiliations

  1. 1.Département de MathématiquesUniversité de Bretagne OccidentaleBrest CedexFrance

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