Harmonic morphisms and Hermitian complex structures on $\mathbb{S}^2 \times \mathbb{S}^2$

Ali Makki (1) , Marina Ville (1)

1 LMPT - Laboratoire de Mathématiques et Physique Théorique

In this paper, we investigate the structure of a harmonic morphism $F$ from $\mathbb{S}^2 \times \mathbb{S}^2$ to a $2$-surface $\mathbb{S}^2$. Baird-Ou construct a family of harmonic morphism from an open set of $\mathbb{S}^2 \times \mathbb{S}^2$ into $\mathbb{S}^2$. We check that they are holomorphic with respect to one of the canonical complex structure.

Domaines: Mathématiques [math]; Géométrie différentielle [math.DG]

Ali Makki, Marina Ville. Harmonic morphisms and Hermitian complex structures on $\mathbb{S}^2 \times \mathbb{S}^2$. 2018. ⟨hal-01922485⟩