When we talk about space-time curvature or the curvature of space, how many different "types" of curvature are there according to GR? For example, the rounded surface of a cylinder is curved in only 1 dimension, while the other is flat. For a sphere, both dimensions of the surface are curved. Since space-time is 4 dimensional, I assume the curvature extends to all 4 dimensions? Also, I've read about intrinsic and extrinsic curvature. Which one does GR predominately deal with?