Concircular geometry of nearly Kähler manifolds

Riemannian manifolds admitting concircular transformations of the metric are considered. Concircular invariants of almost Hermitian manifolds are investigated. The geometry of almost Hermitian manifolds obtained by concircular transformations of the metric of nearly Kähler manifolds is studied in detail. New examples of almost Hermitian manifolds of constant curvature in the class $W_1\oplus W_4$ with integrable as well as non-integrable structure are presented.