Quadratic harmonic morphisms between semi-Riemannian manifolds (Q1943342)

Harmonic morphisms (HMs) between (semi-)Riemannian manifolds \(M\) and \(N\) are smooth maps from \(M\) to \(N\) which pull back local harmonic functions on \(N\) to local harmonic functions on \(M\) [\textit{P. Baird} and \textit{J. C. Wood}, Harmonic morphisms between Riemannian manifolds. Oxford: Oxford University Press (2003; Zbl 1055.53049)]. The classification of quadratic harmonic morphisms (QHMs) between semi-Euclidean spaces given by Lu and Fang is generalized here. The author gives some necessary and sufficient conditions for a homogeneous quadratic map between semi-Euclidean spaces to be a QHM. Also, under certain conditions satisfied by QHMs between semi-Euclidean spaces, three classification results are obtained. Some examples are given as well.