metric torsion
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Torsion 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… … Wikipedia
Metric connection — In mathematics, a metric connection is a connection in a vector bundle E equipped with a metric for which the inner product of any two vectors will remain the same when those vectors are parallel transported along any curve. Other common… … Wikipedia
Metric tensor (general relativity) — This article is about metrics in general relativity. For a discussion of metrics in general, see metric tensor. Metric tensor of spacetime in general relativity written as a matrix. In general relativity, the metric tensor (or simply, the metric) … Wikipedia
Metric compatibility — This article is about the concept in Riemannian geometry. For the typographic concept, see Typeface#Font metrics. In mathematics, given a metric tensor gab, a covariant derivative is said to be compatible with the metric if the following… … Wikipedia
Einstein–Cartan theory — in theoretical physics extends general relativity to correctly handle spin angular momentum. As the master theory of classical physics general relativity has one known flaw: it cannot describe spin orbit coupling , i.e., exchange of intrinsic… … Wikipedia
Affine 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… … Wikipedia
Fundamental theorem of Riemannian geometry — In Riemannian geometry, the fundamental theorem of Riemannian geometry states that on any Riemannian manifold (or pseudo Riemannian manifold) there is a unique torsion free metric connection, called the Levi Civita connection of the given metric … Wikipedia
Differential 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:… … Wikipedia
AMX-30 — French AMX 30B2 sporting a 105 rifled tank gun Type Main battle tank Place of origin … Wikipedia
Connection form — In mathematics, and specifically differential geometry, a connection form is a manner of organizing the data of a connection using the language of moving frames and differential forms. Historically, connection forms were introduced by Élie Cartan … Wikipedia
Levi-Civita connection — In Riemannian geometry, the Levi Civita connection is the torsion free Riemannian connection, i.e., the torsion free connection on the tangent bundle (an affine connection) preserving a given (pseudo )Riemannian metric.The fundamental theorem of… … Wikipedia
