Dark matter as a Ricci soliton

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.