nLab affine connection

Context

Differential cohomology

differential cohomology

Contents

Definition

An affine connection $\nabla$ on a smooth manifold $M$ is a connection on the frame bundle $F M$ of $M$, i. e. the principal bundle of frames in the tangent bundle $T M$.

The components of the local Lie-algebra valued 1-form of an affine connection are called Christoffel symbols.

References

Revised on September 22, 2013 17:12:57 by Urs Schreiber (89.204.139.76)