Bejan, C. L.; Benyounes, M. Harmonic \(\varphi\)-morphisms. (English) Zbl 1045.53044 Beitr. Algebra Geom. 44, No. 2, 309-321 (2003). 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. Reviewer: Vladimir Balan (Bucureşti) Cited in 3 Documents 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 Keywords:harmonic morphism; harmonic map; complete lift metric; tangent bundle; \(\varphi\)-morphism PDFBibTeX XMLCite \textit{C. L. Bejan} and \textit{M. Benyounes}, Beitr. Algebra Geom. 44, No. 2, 309--321 (2003; Zbl 1045.53044) Full Text: EuDML EMIS