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searching for Pseudo-Riemannian manifold 10 found (194 total)

alternate case: pseudo-Riemannian manifold

Normal coordinates (1,319 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

Cotton tensor (1,003 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 (1,058 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

Second covariant derivative (616 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) (775 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 1 2 Δ ⟨ X , X ⟩ = ⟨ ∇ X , ∇ X ⟩ −

Classification theorem (675 words) [view diff] no match in snippet view article find links to article

differential geometry Classification of Riemannian symmetric spaces – (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

Measure (mathematics) (5,554 words) [view diff] no match in snippet view article

angle measure) and has similar uniqueness properties. Every (pseudo) Riemannian manifold ( M , g ) {\displaystyle (M,g)} has a canonical measure μ g {\displaystyle

Lagrangian (field theory) (5,951 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 (6,168 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