Main Question or Discussion Point
Hi, I was wondering if someone wouldn't mind breaking down the geometrical differences between the Riemann, Ricci, and Weyl tensor. My current understanding is that the Ricci tensor describes the change in volume of a n-dimensional object in curved space from flat Euclidean space and that if we have a vanishing Weyl tensor that the space is conformally flat. However, I have a feeling these are 'rough' understandings and would just like to have a more solid concept of them. Oh, and in addition to these 3 tensors, does the Ricci scalar describe something else altogether? Thanks for any clarification!