Metric tensor

The metric tensor is a fundamental concept in differential geometry and plays a key role in the theory of general relativity. It is a mathematical object that describes the geometry of a manifold, allowing one to measure distances and angles on that manifold. ### Definition In a more formal sense, the metric tensor is a type of tensor that defines an inner product on the tangent space at each point of the manifold. This inner product allows one to compute lengths of curves and angles between vectors. ### Properties 1.