Taking the flat rotation curve as input and treating the matter content in the galactic halo region as perfect fluid we obtain a space-time metric at the galactic halo region in the framework of general relativity. We find that the resultant space-time metric is a non-relativistic dark matter induced space-time embedded in a static Friedmann-Lemaître-Robertson-Walker universe i.e. the flat rotation curve not only leads to the existence of dark matter but also suggests about the background geometry of the universe. Within its range of validity the flat rotation curve and the demand that the dark matter to be non-exotic together indicate for a (nearly) flat universe as favored by the modern cosmological observations. We obtain the expressions for energy density and pressure of dark matter there and consequently the equation of state of dark matter. Various other aspects of the solutions are also analyzed.