Curvature Tensor

The curvature tensor is a mathematical tool used in differential geometry to describe how a space bends or twists. It captures how vectors change as they move along curves within that space, revealing the underlying geometric structure. Think of it as a way to measure the way distances and angles are distorted by the space's curvature, such as in the surface of Earth or in spacetime around a massive object. The curvature tensor provides detailed, quantitative information about the bending at each point, enabling us to understand complex geometric and physical phenomena.