Riemann curvature is a mathematical concept that measures the intrinsic curvature of a Riemannian manifold, providing insight into the geometric properties of curved spaces. It plays a crucial role in understanding how matter and energy influence the curvature of spacetime, as described by the Einstein field equations. The Riemann curvature tensor encapsulates how vectors change when they are parallel transported around a loop in the manifold, revealing important information about the gravitational field in general relativity.
congrats on reading the definition of Riemann Curvature. now let's actually learn it.