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...

property of space and time or four-dimensional spacetime. In particular, the curvature of spacetime is directly related to the energy and momentum of whatever...

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

geometry, the center of curvature of a curve is found at a point that is at a distance from the curve equal to the radius of curvature lying on the normal...

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

Additionally, the radius can be estimated from the curvature of the Earth at a point. Like a torus, the curvature at a point will be greatest (tightest) in one...

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

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

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...

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...

directly adapted to the scalar curvature along the Ricci flow.[H88] In general dimensions, he showed that the Riemann curvature tensor satisfies a complicated...

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

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...

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

Spherical Earth or Earth's curvature refers to the approximation of the figure of the Earth as a sphere. The earliest documented mention of the concept...

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...

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...

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

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

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...

best approximates the curvature of a curve at a specific point. It is tangent to the curve at that point and has the same curvature as the curve at that...

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...

and curvature. The following articles provide some useful introductory material: Metric tensor Riemannian manifold Levi-Civita connection Curvature Riemann...

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...

largely reduces the study of complete manifolds of non-negative sectional curvature to that of the compact case. Jeff Cheeger and Detlef Gromoll proved the...

also known as the trace-reversed Ricci tensor) is used to express the curvature of a pseudo-Riemannian manifold. In general relativity, it occurs in the...

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...