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searching for riemann curvature tensor 10 found (184 total)

alternate case: Riemann curvature tensor

Ricci decomposition (1,849 words) [view diff] exact match in snippet view article find links to article

geometry, the Ricci decomposition is a way of breaking up the Riemann curvature tensor of a Riemannian or pseudo-Riemannian manifold into pieces with

Monochromatic electromagnetic plane wave (3,516 words) [view diff] exact match in snippet view article find links to article

sectional curvature). In contrast, the Bel decomposition of the Riemann curvature tensor, taken with respect to X → = e → 0 {\displaystyle {\vec {X}}={\vec

Newton–Cartan theory (1,255 words) [view diff] exact match in snippet view article find links to article

γμν{\displaystyle \gamma ^{\mu \nu }} under Galilei-transformations. The Riemann curvature tensor in inertial system coordinates of this connection is then given

Contributors to the mathematical background for general relativity (260 words) [view diff] exact match in snippet view article find links to article

differential geometry) Georg Bernhard Riemann (Riemannian geometry, Riemann curvature tensor) Richard Schoen (Yamabe problem; see also parent list) Corrado

Weitzenböck identity (832 words) [view diff] exact match in snippet view article find links to article

)\#,\#\rangle +\operatorname {Ric} (\theta ,\#),} where R is the Riemann curvature tensor, Ric is the Ricci tensor, θ : T ∗ M ⊗ Ω p M → Ω p + 1 M {\displaystyle

Electrovacuum solution (1,868 words) [view diff] exact match in snippet view article find links to article

gab{\displaystyle g_{ab}} (or by defining a frame field). The Riemann curvature tensor Rabcd{\displaystyle R_{abcd}} of this manifold and associated quantities

Jordan and Einstein frames (1,103 words) [view diff] exact match in snippet view article find links to article

{g}}_{\mu \nu }} . This means that if we were to reconstruct the Riemann curvature tensor by measurements of geodesic deviation, we would in fact obtain

Tensor software (1,988 words) [view diff] exact match in snippet view article find links to article

coordinates used, TensoriaCalc can compute Christoffel symbols, the Riemann curvature tensor, and Ricci tensor/scalar; it allows for user-defined tensors and

Tetradic Palatini action (4,656 words) [view diff] exact match in snippet view article find links to article

extra term vanishes by symmetries of the Riemann tensor. The usual Riemann curvature tensor R α β γ δ {\displaystyle {R_{\alpha \beta \gamma }}^{\delta }}

Alternatives to general relativity (13,764 words) [view diff] exact match in snippet view article find links to article

(allows the Lagrangian to depend on second-order contractions of the Riemann curvature tensor) f(R) gravity (allows the Lagrangian to depend on higher powers