Curvature of Riemannian manifolds

Curvature in the context of Riemannian manifolds is a fundamental concept in differential geometry that describes how a manifold bends or deviates from being flat. In a more intuitive sense, curvature provides a way to measure how the geometry of a manifold differs from that of Euclidean space. Here are some key aspects of curvature in Riemannian manifolds: ### 1.