Curvature of a measure information

mathematics, the curvature of a measure defined on the Euclidean plane R2 is a quantification of how much the measure's "distribution of mass" is "curved"...

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

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

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...

invariant of Riemannian metrics which measures the failure of the second covariant derivatives to commute. A Riemannian manifold has zero curvature if and...

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

mathematics, the Menger curvature of a triple of points in n-dimensional Euclidean space Rn is the reciprocal of the radius of the circle that passes through...

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

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 Riemannian...

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 approximates...

constrained by curvature). General relativity explains how spatial curvature (local geometry) is constrained by gravity. The global topology of the universe...

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

four-dimensional spacetime. In particular, the curvature of spacetime is directly related to the energy and momentum of whatever matter and radiation are present...

kilometres (3,959 mi). Other ways to define and measure the Earth's radius involve the radius of curvature. A few definitions yield values outside the range...

differential geometry, the Weyl curvature tensor, named after Hermann Weyl, is a measure of the curvature of spacetime or, more generally, a pseudo-Riemannian manifold...

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

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 dates from...

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...

50–300 mGy of radiation due to these radiographs during this time period. The standard method for assessing the curvature quantitatively is measuring the Cobb...

_{1}'(t)\right\|}}.} The first generalized curvature χ1(t) is called curvature and measures the deviance of γ from being a straight line relative to the osculating...

modifications. The curvature of a Riemannian manifold can be described in various ways; the most standard one is the curvature tensor, given in terms of a Levi-Civita...

curvature of the measuring spoon being used and largely upon the physical properties of the substance being measured, and so is not a precise unit of...

an affine connection are its torsion and its curvature. The torsion measures how closely the Lie bracket of vector fields can be recovered from the affine...

to measure the curvature of the surface of a lens. A spherometer usually consists of: A frame with three legs, arranged in an equilateral triangle of known...

A wavefront curvature sensor is a device for measuring the aberrations of an optical wavefront. Like a Shack–Hartmann wavefront sensor it uses an array...

The theorem says that Gaussian curvature can be determined entirely by measuring angles, distances and their rates on a surface, without reference to the...

(métron) 'a measure') is a branch of mathematics concerned with properties of space such as the distance, shape, size, and relative position of figures...

Darboux vector provides a concise way of interpreting curvature κ and torsion τ geometrically: curvature is the measure of the rotation of the Frenet frame about...