curvature matrix
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Curvature — In mathematics, curvature refers to any of a number of loosely related concepts in different areas of geometry. Intuitively, curvature is the amount by which a geometric object deviates from being flat, or straight in the case of a line, but this … Wikipedia
Curvature of Riemannian manifolds — In mathematics, specifically differential geometry, the infinitesimal geometry of Riemannian manifolds with dimension at least 3 is too complicated to be described by a single number at a given point. Riemann introduced an abstract and rigorous… … Wikipedia
Curvature form — In differential geometry, the curvature form describes curvature of a connection on a principal bundle. It can be considered as an alternative to or generalization of curvature tensor in Riemannian geometry. Contents 1 Definition 1.1 Curvature… … Wikipedia
Radius of curvature (applications) — The distance from the center of a sphere or ellipsoid to its surface is its radius. The equivalent surface radius that is described by radial distances at points along the body s surface is its radius of curvature (more formally, the radius of… … Wikipedia
Principal curvature — Saddle surface with normal planes in directions of principal curvatures In differential geometry, the two principal curvatures at a given point of a surface are the eigenvalues of the shape operator at the point. They measure how the surface… … Wikipedia
Ray transfer matrix analysis — (also known as ABCD matrix analysis) is a type of ray tracing technique used in the design of some optical systems, particularly lasers. It involves the construction of a ray transfer matrix which describes the optical system; tracing of a light… … Wikipedia
Gaussian curvature — In differential geometry, the Gaussian curvature or Gauss curvature of a point on a surface is the product of the principal curvatures, κ 1 and κ 2, of the given point. It is an intrinsic measure of curvature, i.e., its value depends only on how… … Wikipedia
Affine curvature — This article is about the curvature of affine plane curves, not to be confused with the curvature of an affine connection. Special affine curvature, also known as the equi affine curvature or affine curvature, is a particular type of curvature… … Wikipedia
Grothendieck–Katz p-curvature conjecture — In mathematics, the Grothendieck–Katz p curvature conjecture is a problem on linear ordinary differential equations, related to differential Galois theory and in a loose sense analogous to the result in the Chebotarev density theorem considered… … Wikipedia
Hessian matrix — In mathematics, the Hessian matrix (or simply the Hessian) is the square matrix of second order partial derivatives of a function; that is, it describes the local curvature of a function of many variables. The Hessian matrix was developed in the… … Wikipedia
Newtonian motivations for general relativity — Some of the basic concepts of General Relativity can be outlined outside the relativistic domain. In particular, the idea that mass/energy generates curvature in space and that curvature affects the motion of masses can be illustrated in a… … Wikipedia
