Examples of affine-metric structures on an almost Hermitian manifold
On an almost Hermitian manifold, we construct an affine subspace of affine connections by using the covariant differential of the almost complex structure on the Riemannian connection of a pseudo-Riemannian metric. We find possible dimensions of this space. For the $8$-dimensional space, we find multidimensional planes of connections that determine post-Riemannian geometries. We also find connections for which the torsion tensor is determined only by the structural tensor or only by the virtual tensor. We fond connections in which the covariant differential of the almost complex structure is determined only by the structural tensor or only by the virtual tensor.