  We provide a possible way of constructing new kinds of manifolds which we
will call Partially Negative Dimensional Product manifold (PNDP-manifold for
short). In particular a PNDP-manifold is an Einstein warped product manifold of
special kind, where the base-manifold $B$ is a Remannian (or pseudo-Riemannian)
product-manifold $B=\Pi_{i=1}^{q'}B_i \times \Pi_{i=(q'+1)}^{\widetilde q}
B_i$, with $\Pi_{i=(q'+1)}^{\widetilde q} B_i$ an Einstein-manifold, and the
fiber-manifold $F$ is a derived-differential-manifold (i.e., $F$ is the form:
smooth manifold ($\mathbb{R}^d$)+ obstruction bundle, so it can admit negative
dimension). Since the dimension of a PNDP-manifold is not related with the
usual geometric concept of dimension, from the speculative and applicative
point of view, we try to define this relation using the concept of desuspension
to identify the PNDP with another kind of "object", introducing a new kind of
hidden dimensions.
