Definitions
from The American Heritage® Dictionary of the English Language, 4th Edition
 n. The act of curving or the state of being curved.
 n. Mathematics The ratio of the change in the angle of a tangent that moves over a given arc to the length of the arc.
 n. Mathematics The limit of this ratio as the length of the arc approaches zero.
 n. Mathematics The reciprocal of the radius of a circle.
 n. Medicine A curving or bending, especially an abnormal one: curvature of the spine.
from Wiktionary, Creative Commons Attribution/ShareAlike License
 n. The shape of something curved.
 n. The extent to which a subspace is curved within a metric space.
 n. The extent to which a Riemannian manifold is intrinsically curved.
from the GNU version of the Collaborative International Dictionary of English
 n. The act of curving, or the state of being bent or curved; a curving or bending, normal or abnormal, as of a line or surface from a rectilinear direction; a bend; a curve.
 n. The amount of degree of bending of a mathematical curve, or the tendency at any point to depart from a tangent drawn to the curve at that point.
from The Century Dictionary and Cyclopedia
 n. Continuous bending; the essential character of a curve: applied primarily to lines, but also to surfaces. See phrases below.
 n. Any curving or bending; a flexure.
 n. Something which is curved or bent.
 n. In projective geometry, susceptibility of being cut in two different points by a straight, independently of whether the construct possessing this property has any point at which two straights inclined to one another and lying in this construct might meet. In metric geometry curvature is often used for the measure of curvature or the reciprocal of the radius of curvature.
from WordNet 3.0 Copyright 2006 by Princeton University. All rights reserved.
 n. the rate of change (at a point) of the angle between a curve and a tangent to the curve
 n. the property possessed by the curving of a line or surface
 n. (medicine) a curving or bending; often abnormal
Etymologies
Examples

The curvature of the spine, spoken of in this work as so common, and as the cause of so many diseases among American women, is what is denominated the _lateral curvature_, and is much more dangerous than the other distortion.
A Treatise on Domestic Economy For the Use of Young Ladies at Home and at School

The Weyl curvature is zero on both the future boundary and past boundary, hence the Big Bang is still welldefined in the cyclic model as the unique hypersurface on which the Weyl curvature vanishes.

It is proposed to abolish the jog, and to swing the east curvature from the east side of Yonge Street opposite College Street southeasterly into Carlton Street at a width of. 100 feet, immediately to the west of the prolongation of Victoria Street, to reduce the width to 80 feet and extend it through at an 80foot width to Jarvis Street.

To make the notion of curvature pathology more precise, we will use the manifestly physical idea of tidal force.

Another common thought, often adverted to in discussion of the two primary notions, is that singular structure, whether in the form of missing points or incomplete paths, must be related to pathological behavior of some sort on the part of the singular spacetime's curvature, that is, the fundamental deformation of spacetime that manifests itself as “the gravitational field.”

The exterior is as pointy as the market demands, but the arch over the entrance is a nice touch, and the door is cut to match its curvature, which is even nicer.

As soon as world lines start to curve, you have to measure their curvature, that is "geodesic curvature".

Newton's law of universal gravitation still holds up well for most circumstances, and it remained unchallenged until Albert Einstein published his general theory of relativity in 1915, in which gravity is defined as the curvature of spacetime.

Spacetime in general relativity is instead said to have intrinsic curvature, which is mathematically quite simple but very difficult to visualize.

The Umtrieb, in other words, does also name a certain curvature of the primordial space of the past where desire constitutes itself, the past in 1815 being itself a "curvature" of the 1811 and
'The Abyss of the Past': Psychoanalysis in Schelling's Ages of the World (1815)
sblowes commented on the word curvature
September 15, 2007