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

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...

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...

have been implemented in the form of Einstein–Cartan theory. Let M be a manifold with an affine connection on the tangent bundle (aka covariant derivative)...

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

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

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...

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

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...

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

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

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...

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...

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

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

Weyl. Élie Cartan introduced the Cartan connection, one of the first concepts of a connection. Levi-Civita defined the Levi-Civita connection, a special...

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...

(globally) CAT(0) space. Cartan (Élie) The mathematician after whom Cartan-Hadamard manifolds, Cartan subalgebras, and Cartan connections are named (not to be...

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

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

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

Newton–Cartan theory (or geometrized Newtonian gravitation) is a geometrical re-formulation, as well as a generalization, of Newtonian gravity first introduced...

Charles-Michel (2007). "The works of Charles Ehresmann on connections: from Cartan connections to connections on fibre bundles". Geometry and Topology of Manifolds...