An Etymological Dictionary of Astronomy and Astrophysics

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.