Riemannian geometry is a branch of differential geometry that studies smooth manifolds equipped with a Riemannian metric. This metric allows for the measurement of geometric properties such as distances, angles, areas, and volumes within the manifold. ### Key Concepts: 1. **Manifolds**: A manifold is a topological space that locally resembles Euclidean space. Riemannian geometry focuses on differentiable manifolds, which have a smooth structure.
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