Tensor field | Wikipedia audio article
Channel: wikipedia tts
Date: 2019-05-10

This is an audio version of the Wikipedia Article:
https://en.wikipedia.org/wiki/Tensor_field


00:01:14 1 Geometric introduction
00:02:20 2 Via coordinate transitions
00:09:25 3 Tensor bundles
00:12:16 4 Notation
00:12:50 5 The iC/isup∞/sup(iM/i) module explanation
00:13:00 6 Applications
00:15:04 7 Tensor calculus
00:16:49 8 Twisting by a line bundle
00:20:38 9 The flat case
00:21:22 10 Cocycles and chain rules
00:22:18 11 Generalizations
00:24:05 11.1 Tensor densities
00:24:57 12 See also
00:26:39 13 Notes
00:26:49 14 References
00:30:35 See also



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SUMMARY
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In mathematics and physics,  a tensor field assigns a tensor to each point of a mathematical space (typically a Euclidean space or manifold). Tensor fields are used in differential geometry, algebraic geometry, general relativity, in the analysis of stress and strain in materials, and in numerous applications in the physical sciences.  As a tensor is a generalization of a scalar (a pure number representing a value, like length) and a vector (a geometrical arrow in space), a tensor field is a generalization of a scalar field or vector field that assigns, respectively, a scalar or vector to each point of space.
Many mathematical structures called "tensors" are tensor fields. For example, the Riemann curvature tensor is not a tensor, as the name implies, but a tensor field: It is named after Bernhard Riemann, and associates a tensor to each point of a Riemannian manifold, which is a topological space.