In mathematics, curvature is any of several strongly related concepts in geometry that intuitively measure the amount by which a curve deviates from being...

In differential geometry, the radius of curvature, R, is the reciprocal of the curvature. For a curve, it equals the radius of the circular arc which best...

defined primarily by its curvature, while the global geometry is characterised by its topology (which itself is constrained by curvature). General relativity...

In differential geometry, the Ricci curvature tensor, named after Gregorio Ricci-Curbastro, is a geometric object which is determined by a choice of Riemannian...

and measure the Earth's radius involve either the spheroid's radius of curvature or the actual topography. A few definitions yield values outside the range...

In the mathematical field of differential geometry, the Riemann curvature tensor or Riemann–Christoffel tensor (after Bernhard Riemann and Elwin Bruno...

geometry, the sectional curvature is one of the ways to describe the curvature of Riemannian manifolds. The sectional curvature K(σp) depends on a two-dimensional...

column is divided into different body regions, which correspond to the curvatures of the vertebral column. The articulating vertebrae are named according...

Gaussian curvature or Gauss curvature Κ of a smooth surface in three-dimensional space at a point is the product of the principal curvatures, κ1 and κ2...

In geometry, the center of curvature of a curve is a point located at a distance from the curve curvature is zero. The osculating circle to the curve is...

term curvature tensor may refer to: the Riemann curvature tensor of a Riemannian manifold — see also Curvature of Riemannian manifolds; the curvature of...

of curvature is a measure of curvature of a circular arc used in civil engineering for its easy use in layout surveying. The degree of curvature is defined...

introduced an abstract and rigorous way to define curvature for these manifolds, now known as the Riemann curvature tensor. Similar notions have found applications...

In mathematics, the mean curvature H {\displaystyle H} of a surface S {\displaystyle S} is an extrinsic measure of curvature that comes from differential...

mathematical field of Riemannian geometry, the scalar curvature (or the Ricci scalar) is a measure of the curvature of a Riemannian manifold. To each point on a...

Spherical Earth or Earth's curvature refers to the approximation of the figure of the Earth to a sphere. The concept of a spherical Earth gradually displaced...

Look up curvature in Wiktionary, the free dictionary. Curvature refers to mathematical concepts in different areas of geometry. Curvature may also refer...

Curvature is a 2017 American science fiction mystery thriller film directed by Diego Hallivis and starring Lyndsy Fonseca and Linda Hamilton. Lyndsy Fonseca...

geometric properties and various quantities associated with them, such as the curvature and the arc length, are expressed via derivatives and integrals using...

geometry, the two principal curvatures at a given point of a surface are the maximum and minimum values of the curvature as expressed by the eigenvalues...

the curvature of spacetime. These tidal accelerations are strictly local. It is the cumulative total effect of many local manifestations of curvature that...

disability. It can be compared to kyphosis and lordosis, other abnormal curvatures of the spine which are in the sagittal plane (front-back) rather than...

Radius of curvature (ROC) has specific meaning and sign convention in optical design. A spherical lens or mirror surface has a center of curvature located...

the Curve of Spee (also called von Spee's curve or Spee's curvature) is defined as the curvature of the mandibular occlusal plane beginning at the canine...

The curvatures of the stomach are the long, convex, lateral surface, and the shorter, concave, medial surface of the stomach, which are referred to as...

Petersburg Mathematical Society for his work on Aleksandrov's spaces of curvature bounded from below. In 1992, he was invited to spend a semester each at...

differential geometry, the curvature form describes curvature of a connection on a principal bundle. The Riemann curvature tensor in Riemannian geometry...

In Riemannian geometry, the geodesic curvature k g {\displaystyle k_{g}} of a curve γ {\displaystyle \gamma } measures how far the curve is from being...

abnormal inward curvature of the lumbar spine. However, the terms lordosis and lordotic are also used to refer to the normal inward curvature of the lumbar...

estimate in the case of the Riemann curvature tensor along a Ricci flow in general dimensions, provided that the curvature operator is nonnegative.[H93b] As...