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Cartan connection - Wikipedia, the free encyclopedia (1518 words) |
 | In mathematics, the Cartan connection construction of differential geometry is a flexible generalisation of the connection concept, developed by Élie Cartan. |
| The main idea is to develop a suitable notion of the connection forms and curvature using moving frames adapted to the particular geometrical problem at hand. |
| The curvature of a Cartan connection is the |
| Levi-Civita connection - Wikipedia, the free encyclopedia (218 words) |
| In Riemannian geometry, the Levi-Civita connection (named for Tullio Levi-Civita) is the torsion-free Riemannian connection, i.e., the torsion-free connection on the tangent bundle preserving a given Riemannian metric (or pseudo-Riemannian metric). |
| In the theory of Riemannian and pseudo-Riemannian manifolds the term covariant derivative is often used for the Levi-Civita connection. |
| The components of this connection with respect to a system of local coordinates are called Christoffel symbols. |
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