Holomorphic foliations, harmonic morphisms and the Walczak formula
A formula of Walczak is applied to two situations in differential geometry. Holomorphic distributions on Kahler manifolds are studied, and it is shown how the formula simplifies to a Bochner type formula, which is particularly useful in the study of integrable distributions. Then the Walczak formula is applied in the context of harmonic morphisms, where it provides a means of investigating the ver
