FACTOID # 66: Australians have a huge 380,000 sq m of land per person - and yet 91% live in urban areas.
 
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Encyclopedia > Affine connection

An affine connection is a connection on the tangent bundle of a differentiable manifold. It can either be torsionless or have non vanishing torsion.


The Levi-Civita connection in Riemannian geometry is an example of an affine connection.




  Results from FactBites:
 
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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