Quadratic harmonic morphisms between semi-Riemannian manifolds

Abstract

In this paper, we study the characterizations and classifications about harmonic morphisms (HMs) between non-degenerate semi-Riemannian manifolds. We establish a necessary and sufficient condition for a quadratic polynomial map between semi-Euclidean spaces to be a HM. Applying this result, we obtain some classifications of quadratic harmonic morphisms (QHMs) under some additional conditions (see Theorem 5.7, Theorem 5.8 and Theorem 6.1), which generalize the results of Ou and Wood for QHMs in Euclidean case (see Ou and Wood (Contrib Algebra Geom 13:41–53, 1996, Ou (Ann Inst Fourier 47(2):687–713, 1997).