nLab
affine connection

Definition

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

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

Related concepts

• connection on a bundle

  • parallel transport, holonomy

• principal connection

  • affine connection, Levi-Civita connection, Cartan connection, symplectic connection

• connection on a 2-bundle

• connection on an infinity-bundle

  • higher parallel transport

References

• wikipedia affine connection
• eom affine connection
• А.П. Норден, Пространства аффинной связности, 1976, djvu