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Harmonic \(\varphi\)-morphisms. (English) Zbl 1045.53044

The authors characterize the harmonicity of \(\varphi\)-morphisms \(\Phi:TM\rightarrow TN\) which cover a map \(\varphi:M\rightarrow N\) between manifolds, when the tangent bundles carry the complete metric. Among numerous other results, it is proved that the mapping \(\varphi\) is a harmonic morphism iff \(d\varphi\) is a harmonic \(\varphi\)-morphism. Examples and applications to \((1,1)\)-tensor fields are provided as well.

MSC:

53C43 Differential geometric aspects of harmonic maps
53C20 Global Riemannian geometry, including pinching
58E20 Harmonic maps, etc.
53C55 Global differential geometry of Hermitian and Kählerian manifolds
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