Singular fibres of harmonic morphisms on [formula omitted

Abstract

In this paper, we study the singular minimal foliation by the fibres of harmonic morphisms due to Burel from (S4,gk,l) into S2 where (gk,l) is a family of conformal metrics on S4. The map arises from a composition of a map to S3 followed by a mapping of Hopf invariant kl. Regular fibres determine a foliation by minimal surfaces which becomes singular at critical points. In order to study the singular set we introduce a notion of multiple fibre and apply 4-dimensional intersection theory.