Almost contact structures and curvature tensors

Abstract

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.