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searching for Pseudo-Riemannian manifold 10 found (190 total)

alternate case: pseudo-Riemannian manifold

Cotton tensor (876 words) [view diff] no match in snippet view article find links to article

In differential geometry, the Cotton tensor on a (pseudo)-Riemannian manifold of dimension n is a third-order tensor concomitant of the metric. The vanishing

Ambient construction (992 words) [view diff] exact match in snippet view article find links to article

manifold, or alternatively as the celestial sphere of a certain pseudo-Riemannian manifold. The ambient construction is canonical in the sense that it is

Normal coordinates (1,200 words) [view diff] exact match in snippet view article find links to article

always exist for the Levi-Civita connection of a Riemannian or Pseudo-Riemannian manifold. By contrast, in general there is no way to define normal coordinates

Second covariant derivative (555 words) [view diff] no match in snippet view article find links to article

respect to another two tangent vector fields. Formally, given a (pseudo)-Riemannian manifold (M, g) associated with a vector bundle E → M, let ∇ denote the

Bochner's theorem (Riemannian geometry) (751 words) [view diff] exact match in snippet view article

{L}}_{X}g)-\operatorname {Ric} (X,\cdot )} holds for any vector field X on a pseudo-Riemannian manifold. As a consequence, there is 12Δ⟨X,X⟩=⟨∇X,∇X⟩−∇Xdiv⁡X+⟨X,div⁡(LXg)⟩−Ric⁡(X

Classification theorem (650 words) [view diff] no match in snippet view article find links to article

geometry Classification of Riemannian symmetric spaces – A (pseudo-)Riemannian manifold whose geodesics are reversible. Classification of 3-dimensional

The Harbor (1,526 words) [view diff] no match in snippet view article find links to article

this painting are embedded in the non-Euclidean Riemannian (or pseudo-Riemannian) manifold of constant positive Gaussian curvature. The surface depicted

Lagrangian (field theory) (5,505 words) [view diff] no match in snippet view article

differential forms, the electromagnetic action S in vacuum on a (pseudo-) Riemannian manifold M{\displaystyle {\mathcal {M}}} can be written (using natural

Lagrangian (field theory) (5,505 words) [view diff] no match in snippet view article

differential forms, the electromagnetic action S in vacuum on a (pseudo-) Riemannian manifold M{\displaystyle {\mathcal {M}}} can be written (using natural

Baker–Campbell–Hausdorff formula (5,643 words) [view diff] no match in snippet view article find links to article

the Lie group is the Cartan metric, the Killing form. For N a (pseudo-)Riemannian manifold, the metric is a (pseudo-)Riemannian metric. A special case of