We determine an orthogonal decomposition of the vector space of some curvature tensors on a co-Hermitian real vector space, in irreducible components with respect to the natural induced representation of \mathcal{U}(
n)×1. One of the components is used to introduce a Bochner curvature tensor on a class of almost co-Hermitian manifolds (or almost contact metric manifolds), called
C(α)-manifolds, containing e.g. co-Kählerian, Sasakian and Kenmotsu manifolds. Other applications of the decomposition are given.
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