2019/09/25 by Nagy, Paul-Andi, Ornea, Liviu
#Differential Geometry (math.DG) #FOS: Mathematics
paper · doi:10.48550/arxiv.1909.11499
We classify both local and global Kähler structures admitting totally geodesic homothetic foliations with complex leaves. The main building blocks are related to Swann's twists and are obtained by applying Weinstein's method of constructing symplectic bundles to Kähler data. As a byproduct we obtain new classes of: holomorphic harmonic morphisms with fibres of arbitrary dimension from compact Kähler manifolds; non-Kähler balanced metrics conformal to Kähler ones (but compatible with different complex structures). Some classes of non-Einstein constant scalar curvature Kähler metrics are also obtained in this way.