Characteristic Properties of Almost Hermitian Structures on Homogeneous Reductive Spaces

Abstract

Homogeneous reductive almost Hermitian spaces are considered. For such spaces satisfying a certain simple algebraic condition, criteria providing simple descriptions of Kahler, nearly Kahler, almost Kahler, quasi-Kahler, and G1 structures are obtained. It is found that, under this condition, Kahler structures can occur only on locally symmetric spaces and nearly Kahler structures, on naturally reductive spaces. Almost Kahler, quasi-Kahler, 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.