**Beiträge zur Algebra und Geometrie / Contributions to Algebra and GeometryVol. 40, No. 1, pp. 1-14 (1999)
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Hermitian Harmonic Maps

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Eric Loubeau

Universite de Bretagne Occidentale, UFR Sciences et Techniques, Departement de Mathematiques, 6, avenue Victor Le Gorgeu; BP 809, 29285 Brest Cedex, France, e-mail: loubeau@univ-brest.fr

**Abstract:** We study the notion of Hermitian harmonicity as introduced by Jost and Yau [JY] in 1993. As a parallel with harmonic maps, we define Hermitian harmonic morphisms, which we characterise as Hermitian harmonic maps satisfying a geometrical condition called biholomorphic horizontal weak conformality. Finally we completely describe maps which mix harmonicity and Hermitian harmonicity by post-composition, and give a few examples.

[JY] Jost, J.; Yau, S. T.: * Harmonic maps and superrigidity.* In R.E. Greene and S.T. Yau, editors: Differential Geometry; Proc. Sympos. Pure Math. ** 54**, 245-280; Amer. Math. Soc., Providence RI, 1993.

**Keywords:** harmonic morphism, Hermitian harmonic

**Classification (MSC91):** 58E20, 53C55

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