On PNDP-manifold

Abstract

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 $B={\Pi }_{i=1}^{q^{\prime }}{B}_i\times {\Pi }_{i=(q^{\prime }+1)}^{\tilde{q}}{B}_i$, with ${\Pi }_{i=(q^{\prime }+1)}^{\tilde{q}}{B}_i$ 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.

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