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Riemann curvature tensor

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 common way used to express the curvature of Riemannian manifolds. It assigns a tensor to each point of a Riemannian manifold (i.e., it is a tensor field). It is a local invariant…

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Overview

Definition

Geometric meaning

Coordinate expression

Symmetries and identities

Ricci curvature

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Riemann curvature tensor

Nodes59
Edges58
Triples25
Avg. degree1.97
Density0.033898
Components1

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Riemann curvature tensor

Top relations

related to Formally · 9
Riemann curvature tensor → Denote, Euclidean, However, Let, Riemannian, The, The Riemann, This, When
related to Definition · 5
Riemann curvature tensor → Let, Levi-Civita, Riemann, Riemannian, We
related to Coordinate expression · 4
Riemann curvature tensor → Christoffel, Converting, Riemann, The
related to Symmetries and identities · 3
Riemann curvature tensor → Bianchi, If, The Riemann
see also · 3
Riemann curvature tensor → Introduction, Riemann, Riemannian
is a · 1
Riemann curvature tensor → way to capture a measure of the intrinsic curvature

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Important terminology

curvature tensor displaystyle riemannian riemann space manifold surface also ricci vector parallel covariant along tennis identities derivative one curved racket

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Riemann curvature tensoris away to capture a measure of the intrinsic curvature0.90text
Riemann curvature tensorrelated to Coordinate expressionConverting0.60section
Riemann curvature tensorrelated to Coordinate expressionRiemann0.60section
Riemann curvature tensorrelated to Coordinate expressionThe0.60section
Riemann curvature tensorrelated to Coordinate expressionChristoffel0.60section
Riemann curvature tensorrelated to DefinitionLet0.60section
Riemann curvature tensorrelated to DefinitionRiemannian0.60section
Riemann curvature tensorrelated to DefinitionWe0.60section
Riemann curvature tensorrelated to DefinitionRiemann0.60section
Riemann curvature tensorrelated to DefinitionLevi-Civita0.60section
Riemann curvature tensorrelated to FormallyWhen0.60section
Riemann curvature tensorrelated to FormallyEuclidean0.60section

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