pseudo-Riemannian geometry, curvature invariants are scalar quantities constructed from tensors that represent curvature. These tensors are usually the...
3 KB (340 words) - 22:54, 11 August 2023
general relativity, curvature invariants are a set of scalars formed from the Riemann, Weyl and Ricci tensors — which represent curvature, hence the name...
7 KB (1,090 words) - 05:51, 27 December 2023
Kretschmann scalar (redirect from Kretschmann invariant)
field tensor Curvature invariant, for curvature invariants in Riemannian and pseudo-Riemannian geometry in general Curvature invariant (general relativity)...
6 KB (1,002 words) - 06:31, 22 August 2024
bi-invariant (that is, simultaneously left- and right-invariant). All left-invariant metrics have constant scalar curvature. Left- and bi-invariant metrics...
59 KB (8,676 words) - 00:25, 8 September 2024
Gaussian curvature or Gauss curvature Κ of a smooth surface in three-dimensional space at a point is the product of the principal curvatures, κ1 and κ2...
19 KB (2,612 words) - 22:21, 7 August 2024
curvature of Riemannian manifolds. It assigns a tensor to each point of a Riemannian manifold (i.e., it is a tensor field). It is a local invariant of...
19 KB (2,911 words) - 19:07, 3 September 2024
The scale-invariant feature transform (SIFT) is a computer vision algorithm to detect, describe, and match local features in images, invented by David...
69 KB (9,197 words) - 00:11, 27 August 2024
scalar curvatures become average values (rather than sums) of sectional curvatures. It is a fundamental fact that the scalar curvature is invariant under...
35 KB (5,029 words) - 23:36, 30 May 2024
translational symmetry are invariant under certain translations. The integral ∫ M K d μ {\textstyle \int _{M}K\,d\mu } of the Gaussian curvature K {\displaystyle...
23 KB (2,760 words) - 17:41, 25 May 2024
physical only after integrating around a closed path, the Berry curvature is a gauge-invariant local manifestation of the geometric properties of the wavefunctions...
15 KB (2,556 words) - 01:34, 10 January 2024
Gaussian curvature of a surface does not change if one bends the surface without stretching it. Thus the Gaussian curvature is an intrinsic invariant of a...
6 KB (685 words) - 19:24, 29 August 2024
In differential geometry, the Ricci curvature tensor, named after Gregorio Ricci-Curbastro, is a geometric object which is determined by a choice of Riemannian...
34 KB (5,859 words) - 04:51, 6 July 2024
Gödel metric (section Curvature invariants)
second invariant means that some observers measure no gravitomagnetism, which is consistent with what was just said. The fact that the first invariant (the...
25 KB (3,884 words) - 17:50, 5 September 2024
to topological invariants and knot type. An old result in this direction is the Fáry–Milnor theorem states that if the total curvature of a knot K in...
10 KB (1,269 words) - 23:58, 31 January 2023
Lorentz scalar (redirect from Lorentz invariant)
theory of physics, a Lorentz scalar is a scalar expression whose value is invariant under any Lorentz transformation. A Lorentz scalar may be generated from...
8 KB (1,406 words) - 09:06, 4 July 2024
Look up affine in Wiktionary, the free dictionary. The principal curvature-based region detector, also called PCBR is a feature detector used in the fields...
7 KB (864 words) - 22:17, 15 November 2022
This relationship between a local geometric invariant, the curvature, and a global topological invariant, the index, is characteristic of results in higher-dimensional...
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constraint: its trace (as used to define the Ricci curvature) must vanish. The Weyl tensor is invariant with respect to a conformal change of metric: if...
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Differentiable curve (redirect from Curvature vector)
differential-geometric invariants called the curvature and the torsion of a curve. The fundamental theorem of curves asserts that the knowledge of these invariants completely...
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Chern–Simons theory (redirect from Witten-Reshetikhin-Turaev invariant)
states. In mathematics, it has been used to calculate knot invariants and three-manifold invariants such as the Jones polynomial. Particularly, Chern–Simons...
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exactly computable Yamabe invariant, and that any Kähler–Einstein metric of negative scalar curvature realizes the Yamabe invariant in dimension 4. It was...
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Weyl tensor (redirect from Weyl curvature tensor)
In differential geometry, the Weyl curvature tensor, named after Hermann Weyl, is a measure of the curvature of spacetime or, more generally, a pseudo-Riemannian...
10 KB (1,742 words) - 17:55, 29 January 2024
Exponential map (Riemannian geometry) (redirect from Bi-invariant metric)
curvature of a surface through p determined by the image under expp of a 2-dimensional subspace of TpM. In the case of Lie groups with a bi-invariant...
9 KB (1,295 words) - 04:38, 2 September 2024
General relativity (redirect from Curvature of space-time)
property of space and time or four-dimensional spacetime. In particular, the curvature of spacetime is directly related to the energy and momentum of whatever...
193 KB (22,603 words) - 03:39, 8 September 2024
p-curvature is an invariant of a connection on a coherent sheaf for schemes of characteristic p > 0. It is a construction similar to a usual curvature,...
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Poincaré metric (redirect from Constant negative curvature)
coordinate: that is, both the Laplace–Beltrami operator and the curvature are invariant under isometries. Thus, for example, let S be a Riemann surface...
10 KB (2,101 words) - 14:58, 4 July 2024
In mathematics, and especially gauge theory, Seiberg–Witten invariants are invariants of compact smooth oriented 4-manifolds introduced by Edward Witten (1994)...
16 KB (2,592 words) - 17:53, 5 November 2023
topological invariant cannot change into each other without a phase transition. The topological invariant is constructed from a curvature function that...
15 KB (1,956 words) - 18:02, 27 April 2024
mathematical physics, vanishing scalar invariant (VSI) spacetimes are Lorentzian manifolds with all polynomial curvature invariants of all orders vanishing. Although...
3 KB (357 words) - 22:24, 28 October 2023
integral of a certain polynomial (the Euler class) of its curvature form (an analytical invariant). It is a highly non-trivial generalization of the classic...
13 KB (1,853 words) - 23:01, 22 May 2024