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gptkbp:instanceOf
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gptkb:mathematical_concept
gptkb:Tensor
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gptkbp:alsoKnownAs
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gptkb:Riemann_curvature_tensor
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gptkbp:component
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R^i_{jkl}
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gptkbp:definedIn
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gptkb:Riemannian_manifold
pseudo-Riemannian manifold
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gptkbp:describes
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curvature of a manifold
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gptkbp:dimensions
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n^2(n^2-1)/12 independent components in n dimensions
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gptkbp:field
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gptkb:general_relativity
differential geometry
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gptkbp:form
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R^i_{jkl} = ∂_k Γ^i_{jl} - ∂_l Γ^i_{jk} + Γ^i_{km}Γ^m_{jl} - Γ^i_{lm}Γ^m_{jk}
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gptkbp:namedAfter
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gptkb:Bernhard_Riemann
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gptkbp:rank
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(1,3) or (0,4)
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gptkbp:relatedTo
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gptkb:metric_tensor
gptkb:Christoffel_symbols
geodesic deviation equation
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gptkbp:symmetry
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antisymmetric in first two indices
antisymmetric in last two indices
satisfies Bianchi identities
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gptkbp:usedIn
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gptkb:Einstein_field_equations
gptkb:Weyl_tensor
gptkb:Ricci_tensor
sectional curvature
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gptkbp:vanishes_for
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flat manifolds
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gptkbp:bfsParent
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gptkb:Weyl_tensor
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gptkbp:bfsLayer
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5
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https://www.w3.org/2000/01/rdf-schema#label
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Riemann tensor
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