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geometry > differential geometry > tensor > metric tensor
algebra > multilinear algebra > tensor > metric tensor

Preferred term

metric tensor  

Definition(s)

  • In the mathematical field of differential geometry, a metric tensor (or simply metric) is an additional structure on a manifold M (such as a surface) that allows defining distances and angles, just as the inner product on a Euclidean space allows defining distances and angles there. More precisely, a metric tensor at a point p of M is a bilinear form defined on the tangent space at p (that is, a bilinear function that maps pairs of tangent vectors to real numbers), and a metric tensor on M consists of a metric tensor at each point p of M that varies smoothly with p.
    (Wikipedia, The Free Encyclopedia, https://en.wikipedia.org/wiki/Metric_tensor)

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