curvature of a surface

curvature of a surface 

A measure of the shape of a curved surface. It is expressed in a unit called reciprocal metre, usually written as m−1, which is equal to the reciprocal of the radius of curvature of a surface in metres. Example: if a surface has a radius of curvature r of +0.5 m, its curvature R will be R = 1/r = 1/+0.5 = 2 m−1.
References in periodicals archive ?
As we show in this paper, the identity for the Gaussian curvature of a surface associated with a first-order ordinary differential equation (ODE) in the first-order jet bundle is described by an inhomogeneous Burgers' equation:
As a new result, we firstly show that the Gaussian curvature of a surface corresponding to a first-order ODE in [J.sup.1] (R, R) is described by nonlinear PDE (1).
Using identity (34) for the Gaussian curvature of a surface corresponding to a given ODE, if we denote the Gaussian curvatures of the surfaces corresponding to equations in (25) by [K.sub.1] and [K.sub.2], respectively, then the theorem follows.