Three-Dimensional Almost Kenmotsu Manifolds Satisfying Certain Nullity Conditions

Abstract

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.