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f-Harmonic morphisms between Riemannian manifolds

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Abstract

f-Harmonic maps were first introduced and studied by Lichnerowicz in 1970. In this paper, the author studies a subclass of f-harmonic maps called f-harmonic morphisms which pull back local harmonic functions to local f-harmonic functions. The author proves that a map between Riemannian manifolds is an f-harmonic morphism if and only if it is a horizontally weakly conformal f-harmonic map. This generalizes the well-known characterization for harmonic morphisms. Some properties and many examples as well as some non-existence of f-harmonic morphisms are given. The author also studies the f-harmonicity of conformal immersions.

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Authors and Affiliations

  1. Department of Mathematics, Guangxi University for Nationalities, Nanning, 530006, China

    Yelin Ou

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  1. Yelin Ou
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Correspondence to Yelin Ou.

Additional information

Project supported by the Guangxi Natural Science Foundation (No. 2011GXNSFA018127).

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Ou, Y. f-Harmonic morphisms between Riemannian manifolds. Chin. Ann. Math. Ser. B 35, 225–236 (2014). https://doi.org/10.1007/s11401-014-0825-0

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  • DOI: https://doi.org/10.1007/s11401-014-0825-0

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