Riemannian geometry is a branch of differential geometry that studies smooth manifolds equipped with a Riemannian metric, which allows for the measurement of distances and angles on these manifolds. This framework provides a way to generalize the concepts of Euclidean geometry to curved spaces, making it crucial for understanding the geometric properties of various surfaces and higher-dimensional spaces. Riemannian geometry is fundamental in physics and mathematics, particularly in the study of general relativity.
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