i am trying to understand the relationship between the two on a local and global scale and how these two concepts are related to the Ricci scalar. Is it correct to say that as far as we know on a global scale, spacetime is flat so that the Ricci scalar is zero. If so, what can be said about the curvature of space alone at a global level, is it also flat? Locally my understanding is that spacetime may be curved due to the presence of massive bodies. In this case is it true to say that both space as well as space time is curved near these bodies? I would assume than the nature of the curvature would depend on the form of the metric that applies locally. Finally, my understanding is that the Ricci tensor and scalar is applicable to spacetime. (is this true?) If so is there an analagous concept in relation to space alone, if that means anything. Are any of the above related to the choice of coordinates? I would have thought not as choice of coordinates should not change the physical reality.