The curvature tensor is a mathematical object that measures the intrinsic curvature of a Riemannian manifold. It encodes how much the geometry of the manifold deviates from being flat and is essential for understanding various geometric properties such as geodesics, curvature, and holonomy. This tensor arises from the Levi-Civita connection and is deeply linked to the study of isometries, sectional curvature, and applications in general relativity.
congrats on reading the definition of Curvature Tensor. now let's actually learn it.