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 (2,490 words) - 22:13, 19 October 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) - 20:15, 30 September 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
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) - 15:42, 3 October 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
(electromagnetic tensor, Maxwell tensor, permittivity, magnetic susceptibility, ...), and general relativity (stress–energy tensor, curvature tensor, ...). In...
69 KB (9,351 words) - 11:28, 12 October 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...
25 KB (4,068 words) - 12:23, 31 October 2024
differential geometry, the Einstein tensor (named after Albert Einstein; also known as the trace-reversed Ricci tensor) is used to express the curvature...
10 KB (1,676 words) - 16:05, 11 October 2024
In mathematics, the signature (v, p, r)[clarification needed] of a metric tensor g (or equivalently, a real quadratic form thought of as a real symmetric...
10 KB (1,334 words) - 00:22, 24 September 2024