An Etymological Dictionary of Astronomy and Astrophysics
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A measure of the amount by which a curve, a surface, or any other manifold deviates from a straight line, a plane, or a hyperplane. In particular, The reciprocal of the radius of the circle which most nearly approximates a curve at a given point.
See also:
→ curvature constant, → curvature of space-time, → field curvature, → primordial curvature perturbation.

From L. curvatura, from curvatus, p.p. of curvare "to bend," from curvus "curved," → curve.

Xamidegi, from xamidé "curved," from xamidag "curved" + noun suffix -i.

A parameter occurring in the → Friedmann equations of → general relativity describing the geometry of → space-time. A spatially → open Universe is defined by k = -1, a → closed Universe by k = + 1 and a → flat Universe by k = 0. See also the → Robertson-Walker metric. See also → curvature of space-time.

→ curvature; → parameter.

According to → general relativity, → space-time is curved by the presence of → matter. The curvature is described in terms of → Riemann's geometry. In → cosmological models three types of curvature are considered: positive (spherical, → closed Universe), zero (Euclidean, → flat Universe), and negative (hyperbolic, → open Universe). See also → curvature constant.

→ curvature; → space-time.

An aberration in an optical instrument, common in Schmidt telescopes, in which the focus changes from the center to the edge of the field of view. Owing to this aberration, a straight object looks curved in the image.

→ field; → curvature.

In cosmological models, the phenomenon that is supposed to seed the → cosmic microwave background anisotropies and the structure formation of the Universe.

→ primordial; → curvature; → perturbation.

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.

→ Riemannian geometry; → curvature; → tensor.

→ curvature of space-time.

→ space; → time; → curvature.