total curvature
11Mean 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… …
12Principal 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… …
13Absolute curvature — Absolute Ab so*lute, a. [L. absolutus, p. p. of absolvere: cf. F. absolu. See {Absolve}.] 1. Loosed from any limitation or condition; uncontrolled; unrestricted; unconditional; as, absolute authority, monarchy, sovereignty, an absolute promise or …
14Gauss–Bonnet theorem — The Gauss–Bonnet theorem or Gauss–Bonnet formula in differential geometry is an important statement about surfaces which connects their geometry (in the sense of curvature) to their topology (in the sense of the Euler characteristic). It is named …
15Inflation (cosmology) — Inflation model and Inflation theory redirect here. For a general rise in the price level, see Inflation. For other uses, see Inflation (disambiguation). Physical cosmology …
16Differential geometry of surfaces — Carl Friedrich Gauss in 1828 In mathematics, the differential geometry of surfaces deals with smooth surfaces with various additional structures, most often, a Riemannian metric. Surfaces have been extensively studied from various perspectives:… …
17Gauss map — In differential geometry, the Gauss map (named after Carl F. Gauss) maps a surface in Euclidean space R3 to the unit sphere S 2. Namely, given a surface X lying in R3, the Gauss map is a continuous map N : X → S 2 such that N ( p ) is a unit… …
18Fary-Milnor theorem — In mathematics, the Fary Milnor theorem in knot theory states that for any knot K in R3, if the total curvature :oint K kappa ,ds leq 4pi then K is an unknot, where kappa is the curvature (it is possible for an unknotted curve to have large total …
19Differential geometry of curves — This article considers only curves in Euclidean space. Most of the notions presented here have analogues for curves in Riemannian and pseudo Riemannian manifolds. For a discussion of curves in an arbitrary topological space, see the main article… …
20Holonomy — Parallel transport on a sphere depends on the path. Transporting from A → N → B → A yields a vector different from the initial vector. This failure to return to the initial vector is measured by the holonomy of the connection. In differential… …
