Abstract: Nearly Kähler- and Kähler-Codazzi-type manifolds are defined in a very similar way. We prove that nearly Kähler-type manifolds make sense only in Hermitian and para-Hermitian contexts, and that Kähler-Codazzi-type manifolds reduce to Kähler-type manifolds in all the four Hermitian, para-Hermitian, Norden and product Riemannian geometries. Kähler-Codazzi condition is also studied on almost complex golden manifolds.

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