Non-holomorphic harmonic morphisms from Kähler manifolds
Given a harmonic morphism \(\psi : N^2 \times M \to \Sigma^2\) in each variable separately, where \(N^2\), \(\Sigma^2\) are surfaces and \(M\) is Riemannian, it has been observed by \textit{J. C. Wood} and the author [Math. Scand. 73, No. 1, 127-155 (1993; Zbl 0790.58009)] that the local smooth solutions \(w = \varphi(p)\) of the equation \(\psi(w,p) = z_0\) define harmonic morphisms. In the present paper the author uses this in various contexts to produce nonholomorphic harmonic morphisms from Kähler manifolds, in particular, from complex Grassmannians.
scientific article; zbMATH DE number 722246