On almost Hermitian structures on 6-dimensional manifolds

Six-dimensional case is special in geometry of almost Hermitian manifolds. This is due to the existence of a well-known Hopf problem on a 6-sphere, the properties of nearly Kaehler manifolds, and a number of other reasons. I’ll talk about some questions and progresses in almost Hermitian geometry, in particular, about the properties of almost Hermitian structures of cohomogeneity 1 on a 6-sphere.