\(fL_k\)-harmonic maps and \(fL_k\)-harmonic morphisms (Q2048954)

The authors define another variant of harmonic maps between manifolds. It is based on the \(L_k\)-harmonic maps involving so-called Newton transformations associated with oriented hypersurfaces. The \(L_k\)-harmonic maps have been introduced in [\textit{M. Aminian} and \textit{S. M. B. Kashani}, Acta Math. Vietnam. 42, No. 3, 471--490 (2017; Zbl 1373.53072)]. The \(fL_k\)-variant defined here is based on writing an additional factor \(f\), assumed to be smooth and positive, into the variational integral. The critical points are called \(fL_k\)-harmonic maps. Defining also the notion of \(fL_k\)-harmonic morphisms, in analogy to harmonic morphism, the authors characterize them in a way that resembles known characterizations of harmonic morphisms.