On harmonic morphisms from $4$-manifolds to Riemann surfaces and local almost Hermitian structures
Résumé
We investigate the structure of a harmonic morphism $F$ from a Riemannian $4$-manifold $M^4$ to a $2$-surface $N^2$ near a critical point $m_0$. If $m_0$ is an isolated critical point or if $M^4$ is compact without boundary, we show that $F$ is pseudo-holomorphic w.r.t. an almost Hermitian structure defined in a neighbourhood of $m_0$. \\ If $M^4$ is compact without boundary, the singular fibres of $F$ are branched minimal surfaces.
Domaines
Géométrie différentielle [math.DG]
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makki.ville.fibres_singulieres_des_morphismes_harmoniques.pdf (162.89 Ko)
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