2014/02/20 by Nordström, Jonas
#58E20 #Differential Geometry (math.DG) #FOS: Mathematics
paper · doi:10.48550/arxiv.1402.4985
We study the curvature of a manifold on which there can be defined a complex-valued submersive harmonic morphism with either, totally geodesic fibers or that is holomorphic with respect to a complex structure which is compatible with the second fundamental form. We also give a necessary curvature condition for the existence of complex-valued harmonic morphisms with totally geodesic fibers on Einstein manifolds.