The curvature tensor of almost cosymplectic and almost Kenmotsu (κ,μ,ν)-spaces

Abstract

We study the Riemann curvature tensor of (κ,μ, ν)-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 (κ,μ, ν)-spaces. We present examples or obstruction results of these spaces in all possible cases.