nLab affine connection

Contents

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

A coordinate-free treatment first appeared in

• Harley Flanders?, Development of an extended exterior differential calculus. Transactions of the American Mathematical Society 75:2 (1953), 311–311. doi.

• wikipedia affine connection

• А.П. Норден, Пространства аффинной связности, 1976, djvu

Last revised on April 3, 2021 at 23:56:26. See the history of this page for a list of all contributions to it.