Are there different kinds of metric in GR? For instance. I read in http://www.astronomy.ohio-state.edu/~dhw/A682/notes3.pdf there the FRW Metric is about: "In 1917, Einstein introduced the first modern cosmological model, based on GR, in which the spatial metric is that of a 3-sphere:" Why. Can the GR metric be based on 2D, 3D, 3-sphere, 3-cube? Can you give other examples? What would happen to the EFE if you change the metric? Btw.. is the FRW metric about space or about spacetime?