Ricci Curvature

Ricci curvature is a mathematical concept from differential geometry that describes how a curved space, such as those studied in Einstein's theory of general relativity, behaves around a point. It generalizes the idea of curvature from surfaces to higher dimensions. Essentially, Ricci curvature measures how much the volume of a small ball in a curved space differs from the volume of a ball in flat space. Positive Ricci curvature indicates that the space is "squeezing" in all directions, while negative curvature suggests a “spreading” out. This concept helps in understanding the shape of the universe and gravitational effects.