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

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.