field of differential geometry, a Cartan connection is a flexible generalization of the notion of an affine connection. It may also be regarded as a specialization...

not fully developed until the early 1920s, by Élie Cartan (as part of his general theory of connections) and Hermann Weyl (who used the notion as a part...

contractions. The significance of the tetradic formalism appear in the Einstein–Cartan formulation of general relativity. The tetradic formalism of the theory...

manifold. A Cartan connection is a way of formulating some aspects of connection theory using differential forms and Lie groups. An Ehresmann connection is a...

Élie Joseph Cartan ForMemRS (French: [kaʁtɑ̃]; 9 April 1869 – 6 May 1951) was an influential French mathematician who did fundamental work in the theory...

In mathematics, the Maurer–Cartan form for a Lie group G is a distinguished differential one-form on G that carries the basic infinitesimal information...

(Cartan's) second structure equation. Historically, the emergence of the structure equations are found in the development of the Cartan connection. When...

In theoretical physics, the Einstein–Cartan theory, also known as the Einstein–Cartan–Sciama–Kibble theory, is a classical theory of gravitation, one of...

and Cartan's equivalence method. Torsion is also useful in the study of unparametrized families of geodesics, via the associated projective connection. In...

b}-\Gamma _{\ \nu \mu }^{\sigma }V_{\sigma }^{\ a}} In the Cartan formalism, the spin connection is used to define both torsion and curvature. These are...

a principal bundle Connection (vector bundle), differentiates a section of a vector bundle along a vector field Cartan connection, achieved by identifying...

moving frames and differential forms. Historically, connection forms were introduced by Élie Cartan in the first half of the 20th century as part of, and...

much the same way as with a covariant derivative. An Ehresmann or Cartan connection supplies a lifting of curves from the manifold to the total space...

projective connection method of moving frames Cartan's equivalence method Vierbein, tetrad Cartan connection applications Einstein–Cartan theory connection (vector...

after Élie Cartan (9 April 1869 – 6 May 1951), a French mathematician. Cartan calculus Cartan connection, Cartan connection applications Cartan's criterion...

relativity), the Levi-Civita connection is the unique affine connection on the tangent bundle of a manifold (i.e. affine connection) that preserves the (pseudo-)Riemannian...

derivative of differential forms by the Cartan formula (also known as the Cartan identity, Cartan homotopy formula or Cartan magic formula): L X ω = d ( ι X ω...

geometry, a projective connection is a type of Cartan connection on a differentiable manifold. The structure of a projective connection is modeled on the geometry...

In conformal differential geometry, a conformal connection is a Cartan connection on an n-dimensional manifold M arising as a deformation of the Klein...

preferred parametrizations on those geodesics. A projective connection is the relevant Cartan connection that gives a means for describing a projective geometry...

In mathematics, Cartan's equivalence method is a technique in differential geometry for determining whether two geometrical structures are the same up...

important applications in the theory of connections on a principal bundle as well as in the theory of Cartan connections. A Lie-algebra-valued differential...

Riemannian connection on a surface or Riemannian 2-manifold refers to several intrinsic geometric structures discovered by Tullio Levi-Civita, Élie Cartan and...

array of numbers describing a metric connection. The metric connection is a specialization of the affine connection to surfaces or other manifolds endowed...

Riemannian holonomy), holonomy of connections in vector bundles, holonomy of Cartan connections, and holonomy of connections in principal bundles. In each...

the Cartan connection. The torsion of the Cartan connection A with respect to the soldering form θ coincides with the torsion of a linear connection Γ,...

mathematician Élie Cartan formulated Einstein's theory in the language of bundles and connections, a generalization of Riemannian geometry to which Cartan made important...

group related to each other. Later, Élie Cartan generalized Klein's homogeneous model spaces to Cartan connections on certain principal bundles, which generalized...

such a connection is equivalently given by a Cartan connection for the affine group of affine space, and is often called an affine connection. The two...

overriding reason to consider connections on associated bundles (as there is, for instance, in the case of Cartan connections) one usually works directly...