Nearly Kähler geometry

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Nearly and almost Kähler manifolds form important classes of almost Hermitian manifolds. They were studied for many years. However, an application of nearly Kähler manifolds in string theory led to a renewed interest in recent years. Aim of the proposed project is a study of nearly and almost Kähler manifolds, which should approach a classification of nearly Kähler manifolds in dimension 6 and a classification of almost Kähler manifolds under additional curvature conditions. The study of these two geometries is unified by the consideration of the canonical Hermitian connection and its properties.