Characteristic Properties of Almost Hermitian Structures on Homogeneous Reductive Spaces

Homogeneous reductive almost Hermitian spaces are considered. For such spaces satisfying a certain simple algebraic condition, criteria providing simple descriptions of Kähler, nearly Kähler, almost Kähler, quasi-Kähler, and G1 structures are obtained. It is found that, under this condition, Kähler structures can occur only on locally symmetric spaces and nearly Kähler structures, on naturally reductive spaces. Almost Kähler, quasi-Kähler, and G1 structures are described by simple conditions imposed on the Nomizu function α of the Riemannian connection of a homogeneous reductive almost Hermitian space.