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Created page with "== Introduction == A Riemannian manifold is a real, smooth manifold M equipped with an inner product g_p on the tangent space T_pM at each point p that varies smoothly from point to point in the sense that if X and Y are differentiable vector fields on M, then p ↦ g_p(X(p), Y(p)) is a smooth function. The Riemannian manifold is a foundational concept in differential geometry and has applications in physics, particularly in the theory of relativity. == Definition =..."
