In a former paper (Cho et al. in Results Math 77:110, 2022. https://doi.org/10.1007/s00025-022-01645-0) the third author introduced the notion of super \(\eta \) -Einstein structure. Then it was proved that a 3-dimensional \(\eta \) -Einstein almost contact metric manifold is super \(\eta \) -Einstein. Moreover, the generalized Sasakian space forms, which include Sasakian space forms, Kenmotsu space forms, and cosymplectic space forms, are super \(\eta \) -Einstein. In this paper, we study interactions between super Einstein almost Hermitian manifolds and super \(\eta \) -Einstein almost contact manifolds. Indeed, for the Boothby–Wang fibration \(\pi : M\rightarrow N\) with a Sasakian manifold \(M^{2n+1}\) and a Kählerian manifold \(N^{2n}\) we prove that M is super \(\eta \) -Einsten if and only if N is super Einstein. Also, we prove that if \(N^{2n}\) admits a Kählerian super Einstein structure, then the warped product \(\mathbb {R}\times _f N\) admits \(\beta \) -Kenmotsu and super \(\eta \) -Einstein structure, where \(f=c\exp (t)\) , \(c\in \mathbb {R}\) . Moreover, we explore the converse. Finally, we focus on a fundamental question on the relation of super \(\eta \) -Einstein manifolds and generalized Sasakian space forms. In particular, we prove that real hypersurfaces of complex space forms are super \(\eta \) -Einstein if and only if they are generalized Sasakian space forms.
