  We consider classes of algebraic manifolds $\mathcal{A}$, of symplectic
manifolds $\mathcal{S}$, of symplectic manifolds with the hard Lefschetz
property $\mathcal{HS}$ and the class of cohomologically symplectic manifolds
$\mathcal{CS}$. For every class of manifolds $\mathcal{C}$ we denote by
$\mathcal{EC}(\pi,n)$ a subclass of $n$-dimensional essential manifolds with
fundamental group $\pi$. In this paper we prove that for all the above classes
with symplectically aspherical form the condition $\mathcal{EC}(\pi,2n)\ne
\emptyset$ implies that $\mathcal{EC}(\pi,2n-2)\ne\emptyset $ for every $n>2$.
Also we prove that all the inclusions
$\mathcal{EA}\subset\mathcal{EHS}\subset\mathcal{ES}\subset\mathcal{ECS}$ are
proper.
