in this article http://en.wikipedia.org/wiki/General_relativity it says in the first paragraph that the curvature of spacetime is related to the stress energy tensor i.e. the matter in the universe. i.e. the curvature at a particular point depends on the matter present at that point. however in this article http://en.wikipedia.org/wiki/Spacetime it says in the section "mathematics of spacetimes" that the metric dictates the geometry of the spacetime. i assume this means that since the metric is dictating the geometry, it is also dictating the curvature. anyway, which is correct? from the Einstein field equations, it would appear to me that both influence the curvature. my interpretation is that since the metric is defined over the entire spacetime it defines the way in which matter will influence the curvature. and then since the mater is obviously different at each point, the matter at that particular point will dictate the curvature(i.e. geometry) at that particular point (with respect to the spacetime metric). is this correct?