Three-dimensional almost Kenmotsu manifolds satisfying certain nullity conditions

TL;DR

This paper studies 3-dimensional almost Kenmotsu manifolds under specific nullity conditions, revealing their structure, equivalences with eta-Einstein conditions, and providing local models and examples of related quasi-Einstein manifolds.

Contribution

It characterizes nullity conditions in 3D almost Kenmotsu manifolds, showing their equivalence to eta-Einstein conditions and constructing local models and examples.

Findings

Nullity conditions coincide with eta-Einstein conditions under certain parameters.

Established local structure descriptions for these manifolds.

Provided examples of N(kappa)-quasi Einstein manifolds.

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.