On generalized \(f\)-harmonic morphisms. (English) Zbl 1313.53075

Cherif, A. Mohammed; Mustapha, Djaa

Commentat. Math. Univ. Carol. 55, No. 1, 17-27 (2014).

The authors study the characterization of generalized \(f\)-harmonic morphisms between Riemannian manifolds. It is proved that a map between Riemannian manifolds is an \(f\)-harmonic morphism if and only if it is a horizontally weakly conformal map satisfying some further conditions. As well, the authors present new properties which generalize the Fuglede-Ishihara characterization for harmonic morphisms [T. Ishihara, J. Math. Kyoto Univ. 19, 215–229 (1979; Zbl 0421.31006); B. Fuglede, Elliptische Differentialgleichungen, Vortr. Tag. Rostock 1977, 97–104 (1978; Zbl 0408.31011)].

Reviewer: Vladimir Balan (Bucureşti)

MSC:

53C43	Differential geometric aspects of harmonic maps
58E20	Harmonic maps, etc.

Keywords:

\(f\)-harmonic morphism; \(f\)-harmonic map; horizontally weakly conformal map

Citations:

Zbl 0421.31006; Zbl 0408.31011