A Riemannian metric is a mathematical structure that defines a way of measuring distances and angles on a manifold, allowing it to behave like a curved space. This metric tensor is a key tool in differential geometry, as it enables the generalization of concepts like length, angle, and curvature in higher-dimensional spaces. The Riemannian metric is essential for understanding how the geometry of the manifold interacts with the physical properties described by equations in various fields such as physics and engineering.
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