Conformal and semi-conformal biharmonic maps |
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Authors: | Paul Baird Ali Fardoun Seddik Ouakkas |
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Affiliation: | (1) Département de Mathématiques, Université de Bretagne Occidentale, 6 Avenue Le Gorgeu, B.P. 452, 29285 Brest Cedex, France |
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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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Keywords: | Conformal map Semi-conformal map Biharmonic map |
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