radius of a principal curvature
1Principal 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… …
2Radius 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… …
3Curvature — 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 …
4curvature — /kerr veuh cheuhr, choor /, n. 1. the act of curving or the state of being curved. 2. a curved condition, often abnormal: curvature of the spine. 3. the degree of curving of a line or surface. 4. Geom. a. (at a point on a curve) the derivative of …
5Curvature 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… …
6Curvature 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… …
7Curvature of a measure — In 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 . It is related to notions of curvature in geometry. In the form presented below, the… …
8Gaussian 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… …
9Scalar curvature — In Riemannian geometry, the scalar curvature (or Ricci scalar) is the simplest curvature invariant of a Riemannian manifold. To each point on a Riemannian manifold, it assigns a single real number determined by the intrinsic geometry of the… …
10Mean curvature — In mathematics, the mean curvature H of a surface S is an extrinsic measure of curvature that comes from differential geometry and that locally describes the curvature of an embedded surface in some ambient space such as Euclidean space. The… …
