Riemann curvature tensor — An Etymological Dictionary of Astronomy and Astrophysics

Riemann curvature tensor

تانسور ِ خمیدگی ِ ریمان

tânsor-e xamidegi-ye Riemann

Fr.: tenseur de courbure de Riemann

A 4th → rank tensor that characterizes the deviation of the geometry of space from the Euclidean type. The curvature tensor
R^λ_μνκ is defined through the → Christoffel symbols Γ^λ_μν as follows:

R^λ_μνκ = (∂Γ^λ_μκ)/(∂x^ν) - (∂Γ^λ_μν)/(∂x^κ) + Γ^η_μκΓ^λ_ην - Γ^η_μνΓ^λ_ηκ.

See also: → Riemannian geometry; → curvature; → tensor.

An Etymological Dictionary of Astronomy and Astrophysics

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