We introduce a novel concept known as the partially negative dimensional product manifold, abbreviated as PNDP-manifold. Specifically, a PNDP-manifold represents a unique form of Einstein sequential warped product manifold, where the base manifold \(\mathscr {B}\) is a Riemannian (or pseudo-Riemannian) product manifold expressed as \( \mathscr {B}= \mathscr {B}_1\times \mathscr {B}_2\) , with \(\mathscr {B}_2\) being an Einstein manifold. The fiber manifold \( \mathscr {F} \) , on the other hand, is treated as a derived smooth manifold, characterized by a Kuranishi neighborhood \( (\mathbb {R}^d, \mathscr {E}, S) \) , where \( \mathscr {E} \) serves as the obstruction bundle and \( S \) is a smooth section. This setup allows for the possibility of a “virtual” dimension, which may even be negative. From the perspective of differential geometry, this particular type of Einstein sequential warped product manifold offers a broader range of exact solutions to Einstein’s field equations, while keeping the computations relatively straightforward, especially when compared to Einstein warped-product manifolds with Ricci-flat fibers \( (\mathscr {F}; \ddot{g}) \) . On a more speculative level, by interpreting the fiber as a derived smooth manifold, the dimensions of a PNDP-manifold extend beyond the traditional geometric understanding of dimension, being instead viewed as “virtual” dimensions. With appropriate interpretation, this concept opens up the possibility of new “hidden” dimensions, which could have intriguing speculative and practical implications. These may include applications in fields like econophysics, where financial markets influenced by ghost fields such as dark volatility could be modeled, or in cosmology, where the idea of “emerging spaces” might be explored.