On harmonic morphisms from 4-manifolds to Riemann surfaces and local almost Hermitian structures

2013/07/15 by Makki, Ali, Ville, Marina
#Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1307.3903

Abstract

We investigate the structure of a harmonic morphism F from a Riemannian 4-manifold M⁴ to a 2-surface N² near a critical point m₀. If m₀ is an isolated critical point or if M⁴ is compact without boundary, we show that F is pseudo-holomorphic w.r.t. an almost Hermitian structure defined in a neighbourhood of m₀. If M⁴ is compact without boundary, the singular fibres of F are branched minimal surfaces.

Related

• Holomorphic harmonic morphisms from cosymplectic almost Hermitian manifolds
• Holomorphic harmonic morphisms from four-dimensional non-Einstein manifolds
• Almost complex structures that are harmonic maps
• Pseudo-harmonic morphisms with low dimensional fibers
• Embedded surfaces and almost complex structures