The curvature tensor of almost cosymplectic and almost Kenmotsu (\kappa,\mu,\nu)-spaces

Abstract

We study the Riemann curvature tensor of (\kappa,\mu,\nu)-spaces when they have almost cosymplectic and almost Kenmotsu structures, giving its writing explicitly. This leads to the definition and study of a natural generalisation of the contact metric (\kappa,\mu,\nu)-spaces. We present examples or obstruction results of these spaces in all possible cases.