mathematical fields of Riemannian and pseudo-Riemannian geometry, the Ricci decomposition is a way of breaking up the Riemann curvature tensor of a Riemannian...

the Ricci decomposition; it is orthogonal to the difference between the Riemann tensor and itself. The other two parts of the Ricci decomposition correspond...

In differential geometry, the Ricci curvature tensor, named after Gregorio Ricci-Curbastro, is a geometric object which is determined by a choice of Riemannian...

decomposed into a Weyl part and a Ricci part. This decomposition is known as the Ricci decomposition, and plays an important role in the conformal geometry...

Gregorio Ricci-Curbastro (Italian: [ɡreˈɡɔːrjo ˈrittʃi kurˈbastro]; 12 January 1853 – 6 August 1925) was an Italian mathematician. He is most famous as...

from the Ricci decomposition of the Riemann tensor into the Weyl tensor plus a sum of fourth-rank tensors constructed from the second rank Ricci tensor...

phrased as saying that Ricci-flatness is characterized by the vanishing of the two non-Weyl parts of the Ricci decomposition. Since the Weyl curvature...

subspace learning Penrose graphical notation Regge calculus Ricci calculus Ricci decomposition Tensor (intrinsic definition) Tensor calculus Tensor field...

geometric analysis, the Ricci flow (/ˈriːtʃi/ REE-chee, Italian: [ˈrittʃi]), sometimes also referred to as Hamilton's Ricci flow, is a certain partial...

\!\!\!\!\!\!\!\!\;\bigcirc ~}g\right|^{2}.} This decomposition, known as the Ricci decomposition, expresses the Riemann curvature tensor into its irreducible...

pseudo-Riemannian geometry in general Curvature invariant (general relativity) Ricci decomposition, for more about the Riemann and Weyl tensor Richard C. Henry (2000)...

magnetic field. Such a decomposition was partially described by Alphonse Matte in 1953 and by Lluis Bel in 1958. This decomposition is particularly important...

follows from the Ricci decomposition of the Riemann curvature tensor as a sum of the Weyl curvature tensor plus terms built out of the Ricci tensor: the Weyl...

is viewed as a 4-dimensional manifold. In terms of the orthogonal Ricci decomposition of the Riemann curvature tensor, this formula can also be written...

Scalar curvature Sectional curvature Ricci curvature, Ricci flat Ricci decomposition Schouten tensor Weyl curvature Ricci flow Einstein manifold Holonomy Gauss–Bonnet...

decomposition, which is not quite the same as the decomposition in the geometrization conjecture, because some of the pieces in the JSJ decomposition...

Statement relating differentiable symmetries to conserved quantities Ricci decomposition Symmetry in physics – Feature of a system that is preserved under...

program of using the Ricci flow to solve the problem. By developing a number of new techniques and results in the theory of Ricci flow, Grigori Perelman...

the Ricci curvature (or rather, the Schouten tensor) and the Weyl tensor each makes to the curvature of a Riemannian manifold. This so-called Ricci decomposition...

Riemann tensor, but leaves the Weyl tensor unspecified (see the Ricci decomposition), the Einstein equation may be considered a kind of compatibility...

decomposition or rank-R decomposition is the decomposition of a tensor as a sum of R rank-1 tensors, where R is minimal. Computing this decomposition...

Einstein field equations must provide the Ricci tensor to complete the components of the Ricci decomposition. The Curtright field has a gauge-transformation...

Lawrence A. Ricci (June 17, 1945 – October 2005) was a reputed Genovese crime family acting capo. Officially a dairy products salesman, Ricci was allegedly...

positivity of Ricci curvature is replaced by a quantitative closeness to constant curvature.[H85] This is measured in terms of the Ricci decomposition. Almost...

Carminati–McLenaghan invariants Curvature invariant (general relativity) Ricci decomposition Stephani, Hans (2009). "9. Invariants and the characterization of...

they are often simply called "tensors". Tullio Levi-Civita and Gregorio Ricci-Curbastro popularised tensors in 1900 – continuing the earlier work of Bernhard...

mathematics of general relativity Decomposition of the Riemann curvature tensor Curvature of Riemannian manifolds Ricci curvature tensor Lee 2018, p. 193...

the Ricci decomposition, splits the Riemann tensor into three pieces, which are each fourth-rank tensors, built out of, respectively, the Ricci scalar...

Riabouchinsky solid Riazuddin (physicist) Riccardo Giacconi Ricci calculus Ricci curvature Ricci decomposition Richard A. Muller Richard Arnowitt Richard Becker...

theorem. TensorDecompositions.jl provides several tensor decomposition approaches. TensorToolbox.jl provides several tensor decomposition approaches. This...