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Conformal and semi-conformal biharmonic maps

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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.

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Authors and Affiliations

  1. Département de Mathématiques, Université de Bretagne Occidentale, 6 Avenue Le Gorgeu, B.P. 452, 29285, Brest Cedex, France

    Paul Baird, Ali Fardoun & Seddik Ouakkas

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  1. Paul Baird
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  2. Ali Fardoun
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  3. Seddik Ouakkas
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Correspondence to Paul Baird.

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Baird, P., Fardoun, A. & Ouakkas, S. Conformal and semi-conformal biharmonic maps. Ann Glob Anal Geom 34, 403–414 (2008). https://doi.org/10.1007/s10455-008-9118-8

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  • DOI: https://doi.org/10.1007/s10455-008-9118-8

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