Riemannian manifold

A Riemannian manifold is a mathematical space that combines concepts from geometry and calculus. Imagine a surface, like a sphere or a donut, where you can measure distances and angles. In this space, the notion of "straight lines" can change based on the curvature, much like how straight roads bend on a globe. This framework allows for the study of complex shapes and spaces, enabling applications in physics, especially in understanding the fabric of the universe in theories like General Relativity. Essentially, Riemannian manifolds help us explore and quantify the geometry of curved spaces.