nLab
affine connection

Contents

Context

\infty-Chern-Weil theory

Differential cohomology

Contents

Definition

An affine connection \nabla on a smooth manifold MM is a connection on the frame bundle FMF M of MM, i.e., the principal bundle of frames in the tangent bundle TMT 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

  • eom 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.