The Riemann curvature tensor

The Riemann curvature tensor is a mathematical tool that measures how a space bends or curves. Imagine walking on a surface; if you walk straight in a flat space, your direction remains unchanged. But on a curved surface, your path might shift unexpectedly, indicating curvature. The tensor captures this by analyzing how vectors change as they move around tiny loops in space. In essence, it provides a detailed description of how space itself is curved, which is fundamental in understanding gravity in Einstein’s theory of General Relativity and the geometry of the universe.