Singular fibres of harmonic morphisms on S4

Ali Makki (1) , Marc Soret (1) , Marina Ville (1)

1 LMPT - Laboratoire de Mathématiques et Physique Théorique

In this paper, we study the singular minimal foliation by the fibres of harmonic morphisms due to Burel from into where is a family of conformal metrics on . The map arises from a composition of a map to 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.

Domaines: Géométrie différentielle [math.DG]

Ali Makki, Marc Soret, Marina Ville. Singular fibres of harmonic morphisms on S4. Differential Geometry and its Applications, 2019, 67, pp.101550. ⟨10.1016/j.difgeo.2019.06.006⟩. ⟨hal-02342149⟩