Three-dimensional almost Kenmotsu manifolds satisfying certain nullity conditions

We investigate 3-dimensional almost Kenmotsu manifolds satisfying special types of nullity conditions depending on two smooth functions $\kappa,\mu$. When either $\kappa<-1$ and $\mu=0$ or $h=0$, such conditions coincide with the $\kappa$-nullity condition which we show to be equivalent to the $\eta$-Einstein one. As an application of this result, we obtain examples of $N(\kappa)$-quasi Einstein manifolds. Moreover, for the aforementioned manifolds, some complete local descriptions of their structure are established, building local "models" for each of them.