Linked from

The 12 pages that link to Affine connection, each with the reason it gives.

• GeodesicRelated: It defines parallel transport, the operation underlying the geodesic equation.

• Differential geometryBroader topic: It makes directional differentiation possible when tangent spaces at different points differ.

• Riemann curvature tensorRelated: A connection supplies the covariant derivatives whose commutator defines curvature.

• Affine spaceRelated: It extends affine ideas about parallel displacement to curved spaces.

• Christoffel symbolsNarrower topic: Christoffel symbols are the local coordinate coefficients of an affine connection.

• Exponential mapRelated: It specifies parallel transport and determines which curves count as geodesics.

• Levi-Civita connectionNarrower topic: The Levi-Civita connection is a uniquely specified affine connection.

• Tensor calculusRelated: Its coefficients supply the correction terms in covariant derivatives.

• Tullio Levi-CivitaRelated: Levi-Civita’s work helped establish connections as tools for expressing geometric differentiation.

• Bianchi identitiesNarrower topic: The identities apply to curvature defined by a connection, not only to a particular coordinate formula.

• Classical unified field theoriesRelated: Some unified theories enlarged the connection to carry electromagnetic degrees of freedom.

• Fundamental theorem of Riemannian geometryNarrower topic: The theorem identifies a distinguished connection on each Riemannian manifold.