Data Portal @ linkeddatafragments.org

Matches in DBpedia 2014 for { <http://dbpedia.org/resource/Riemann_curvature_tensor> ?p ?o. }

• Riemann_curvature_tensor abstract "In the mathematical field of differential geometry, the Riemann curvature tensor, or Riemann–Christoffel tensor after Bernhard Riemann and Elwin Bruno Christoffel, is the most standard way to express curvature of Riemannian manifolds. It associates a tensor to each point of a Riemannian manifold (i.e., it is a tensor field), that measures the extent to which the metric tensor is not locally isometric to a Euclidean space. The curvature tensor can also be defined for any pseudo-Riemannian manifold, or indeed any manifold equipped with an affine connection. It is a central mathematical tool in the theory of general relativity, the modern theory of gravity, and the curvature of spacetime is in principle observable via the geodesic deviation equation. The curvature tensor represents the tidal force experienced by a rigid body moving along a geodesic in a sense made precise by the Jacobi equation.The curvature tensor is given in terms of the Levi-Civita connection by the following formula:where [u,v] is the Lie bracket of vector fields. For each pair of tangent vectors u, v, R(u,v) is a linear transformation of the tangent space of the manifold. It is linear in u and v, and so defines a tensor. Occasionally, the curvature tensor is defined with the opposite sign.If and are coordinate vector fields then and therefore the formula simplifies to The curvature tensor measures noncommutativity of the covariant derivative, and as such is the integrability obstruction for the existence of an isometry with Euclidean space (called, in this context, flat space). The linear transformation is also called the curvature transformation or endomorphism.The curvature formula can also be expressed in terms of the second covariant derivative defined as: which is linear in u and v. Then: Thus in the general case of non-coordinate vectors u and v, the curvature tensor measures the noncommutativity of the second covariant derivative.".
• Riemann_curvature_tensor wikiPageID "130526".
• Riemann_curvature_tensor wikiPageRevisionID "598328393".
• Riemann_curvature_tensor hasPhotoCollection Riemann_curvature_tensor.
• Riemann_curvature_tensor subject Category:Curvature_(mathematics).
• Riemann_curvature_tensor subject Category:Riemannian_geometry.
• Riemann_curvature_tensor subject Category:Tensors_in_general_relativity.
• Riemann_curvature_tensor type Abstraction100002137.
• Riemann_curvature_tensor type Cognition100023271.
• Riemann_curvature_tensor type Concept105835747.
• Riemann_curvature_tensor type Content105809192.
• Riemann_curvature_tensor type Idea105833840.
• Riemann_curvature_tensor type PsychologicalFeature100023100.
• Riemann_curvature_tensor type Quantity105855125.
• Riemann_curvature_tensor type Tensor105864481.
• Riemann_curvature_tensor type TensorsInGeneralRelativity.
• Riemann_curvature_tensor type Variable105857459.
• Riemann_curvature_tensor comment "In the mathematical field of differential geometry, the Riemann curvature tensor, or Riemann–Christoffel tensor after Bernhard Riemann and Elwin Bruno Christoffel, is the most standard way to express curvature of Riemannian manifolds. It associates a tensor to each point of a Riemannian manifold (i.e., it is a tensor field), that measures the extent to which the metric tensor is not locally isometric to a Euclidean space.".
• Riemann_curvature_tensor label "Krommingstensor van Riemann".
• Riemann_curvature_tensor label "Riemann curvature tensor".
• Riemann_curvature_tensor label "Riemannscher Krümmungstensor".
• Riemann_curvature_tensor label "Tenseur de Riemann".
• Riemann_curvature_tensor label "Tensor de curvatura".
• Riemann_curvature_tensor label "Tensor de curvatura".
• Riemann_curvature_tensor label "Tensor krzywizny Riemanna".
• Riemann_curvature_tensor label "Tensore di Riemann".
• Riemann_curvature_tensor label "Тензор кривизны".
• Riemann_curvature_tensor label "リーマン曲率テンソル".
• Riemann_curvature_tensor label "黎曼曲率張量".
• Riemann_curvature_tensor sameAs Riemannscher_Krümmungstensor.
• Riemann_curvature_tensor sameAs Τανυστής_καμπυλότητας_Riemann.
• Riemann_curvature_tensor sameAs Tensor_de_curvatura.
• Riemann_curvature_tensor sameAs Tenseur_de_Riemann.
• Riemann_curvature_tensor sameAs Tensore_di_Riemann.
• Riemann_curvature_tensor sameAs リーマン曲率テンソル.
• Riemann_curvature_tensor sameAs 리만_곡률_텐서.
• Riemann_curvature_tensor sameAs Krommingstensor_van_Riemann.
• Riemann_curvature_tensor sameAs Tensor_krzywizny_Riemanna.
• Riemann_curvature_tensor sameAs Tensor_de_curvatura.
• Riemann_curvature_tensor sameAs m.0z9c5.
• Riemann_curvature_tensor sameAs Q855112.
• Riemann_curvature_tensor sameAs Q855112.
• Riemann_curvature_tensor sameAs Riemann_curvature_tensor.
• Riemann_curvature_tensor wasDerivedFrom Riemann_curvature_tensor?oldid=598328393.
• Riemann_curvature_tensor isPrimaryTopicOf Riemann_curvature_tensor.