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)...
56 KB (8,866 words) - 08:52, 9 August 2024
differentiable manifold M {\displaystyle M} and the metric tensor is given as a covariant, second-degree, symmetric tensor on M {\displaystyle M} , conventionally...
15 KB (2,488 words) - 23:03, 29 December 2023
In mathematics, tensor calculus, tensor analysis, or Ricci calculus is an extension of vector calculus to tensor fields (tensors that may vary over a manifold...
13 KB (1,906 words) - 17:49, 5 July 2024
the Riemann tensor. This tensor has the same symmetries as the Riemann tensor, but satisfies the extra condition that it is trace-free: metric contraction...
10 KB (1,742 words) - 17:55, 29 January 2024
Ricci curvature (redirect from Ricci curvature tensor)
geometry of a given metric tensor differs locally from that of ordinary Euclidean space or pseudo-Euclidean space. The Ricci tensor can be characterized...
34 KB (5,859 words) - 04:51, 6 July 2024
In multilinear algebra, a tensor contraction is an operation on a tensor that arises from the canonical pairing of a vector space and its dual. In components...
13 KB (1,882 words) - 15:56, 12 January 2024
differential geometry, the Einstein tensor (named after Albert Einstein; also known as the trace-reversed Ricci tensor) is used to express the curvature...
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(electromagnetic tensor, Maxwell tensor, permittivity, magnetic susceptibility, ...), and general relativity (stress–energy tensor, curvature tensor, ...). In...
69 KB (9,354 words) - 17:48, 12 July 2024
stress-energy tensor The stress–energy tensor, sometimes called the stress–energy–momentum tensor or the energy–momentum tensor, is a tensor physical quantity...
23 KB (3,997 words) - 16:35, 1 August 2024
It assigns a tensor to each point of a Riemannian manifold (i.e., it is a tensor field). It is a local invariant of Riemannian metrics which measures...
19 KB (2,904 words) - 22:21, 30 June 2024