  In this paper we consider clumped baryonic matter as a spherically symmetric
barotropic fluid associated with a compact four-dimensional Einstein manifold
with a four-radius that is determined by the fluid density. We further
investigate the properties of these matter generated manifolds and show that
because of their homogeneity and isotropy they exhibit FLRW metric properties
and expand with cosmic time. At low densities such as those encountered in star
clusters, galaxies and galactic clusters, these manifolds are large and show
the same properties that are currently attributed to dark matter.
