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 c U(n)xl.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(ά)-manifolds, containing e.g.co-Kahlerian, Sasakian and Kenmotsu manifolds.Other applications of the decomposition are given.