Timeline for Geometric interpretation of the Weyl tensor?
Current License: CC BY-SA 4.0
8 events
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| Aug 11, 2020 at 16:20 | vote | accept | Tim Campion | ||
| Aug 9, 2020 at 13:40 | comment | added | Ben McKay | Penrose has some way of thinking about the Weyl tensor geometrically, but only for Lorentzian signature 4-manifolds, if I remember correctly, but I think his approach splits into self-dual and anti-self-dual parts first, and then gives each one an interpretation. | |
| Aug 8, 2020 at 21:02 | history | edited | Tim Campion | CC BY-SA 4.0 |
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| Aug 7, 2020 at 0:50 | answer | added | Jeffrey Case | timeline score: 18 | |
| Aug 6, 2020 at 18:57 | comment | added | Pedro Lauridsen Ribeiro | One aspect which is important to have in mind when dealing with the Weyl tensor is that due to its algebraic symmetries it identically vanishes if the manifold dimension is less than four. In three dimensions there is another conformal tensor built from the metric and its derivatives, called the Bach tensor, which shares many of the properties of the Weyl tensor. In Lorentzian geometry, the importance of the Weyl tensor also lies on the fact that, on space-times solving the Einstein equations, the Weyl tensor encodes all dynamically propagating degrees of freedom (e.g. gravitational waves). | |
| Aug 6, 2020 at 18:31 | history | edited | Tim Campion | CC BY-SA 4.0 |
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| Aug 6, 2020 at 18:22 | history | edited | Tim Campion | CC BY-SA 4.0 |
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| Aug 6, 2020 at 17:54 | history | asked | Tim Campion | CC BY-SA 4.0 |