torsion-free frame
1Torsion tensor — In differential geometry, the notion of torsion is a manner of characterizing a twist or screw of a moving frame around a curve. The torsion of a curve, as it appears in the Frenet Serret formulas, for instance, quantifies the twist of a curve… …
2torsion bar — A long spring steel rod attached in such a way that one end is anchored while the other is free to twist. One end is fastened to the frame at one end and to a suspension part at the other. If an arm is attached, at right angles, to the free end,… …
3Moving frame — The Frenet Serret frame on a curve is the simplest example of a moving frame. In mathematics, a moving frame is a flexible generalization of the notion of an ordered basis of a vector space often used to study the extrinsic differential geometry… …
4Affine connection — An affine connection on the sphere rolls the affine tangent plane from one point to another. As it does so, the point of contact traces out a curve in the plane: the development. In the branch of mathematics called differential geometry, an… …
5G-structure — In differential geometry, a G structure on an n manifold M , for a given structure group [Which is a Lie group G o GL(n,mathbf{R}) mapping to the general linear group GL(n,mathbf{R}). This is often but not always a Lie subgroup; for instance, for …
6Differential 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:… …
7Mathematics of general relativity — For a generally accessible and less technical introduction to the topic, see Introduction to mathematics of general relativity. General relativity Introduction Mathematical formulation Resources …
8Holonomy — 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… …
9Covariant derivative — In mathematics, the covariant derivative is a way of specifying a derivative along tangent vectors of a manifold. Alternatively, the covariant derivative is a way of introducing and working with a connection on a manifold by means of a… …
10Cartan connection applications — This page covers applications of the Cartan formalism. For the general concept see Cartan connection.Vierbeins, et cetera The vierbein or tetrad theory much used in theoretical physics is a special case of the application of Cartan connection in… …
