Abstract
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 G 1 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 G 1 structures are described by simple conditions imposed on the Nomizu function α of the Riemannian connection of a homogeneous reductive almost Hermitian space.
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Dashevich, O.V. Characteristic Properties of Almost Hermitian Structures on Homogeneous Reductive Spaces. Mathematical Notes 73, 636–642 (2003). https://doi.org/10.1023/A:1024056520339
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DOI: https://doi.org/10.1023/A:1024056520339