Harmonic morphisms from complex projective spaces (Q1345114)

According to a result of \textit{J. C. Wood} [Int. J. Math. 3, No. 3, 415- 439 (1992; Zbl 0763.53051)], a locally defined harmonic morphism \(\varphi : \mathbb{C} P^2 \to N^2\) to a Riemann surface \(N^2\) is holomorphic with respect to a (locally defined) Hermitian structure. The author constructs here locally defined harmonic morphisms \(\varphi: \mathbb{C} P^m \to S^2\), \(m \geq 3\), that are not holomorphic with respect to the standard Kähler structure on \(\mathbb{C} P^m\).