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 $κ,μ$. When either $κ<-1$ and $μ=0$ or $h=0$, such conditions coincide with the $κ$-nullity condition which we show to be equivalent to the $η$-Einstein one. As an application of this result, we obtain examples of $N(κ)$-quasi Einstein manifolds. Moreover, for the aforementioned manifolds, some complete local descriptions of their structure are established, building local "models" for each of them.

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