Differential geometry MOC

Lie derivative

Let be a vector field generating the flow . The Lie derivative

is an -linear map defined by¹ #m/def/geo/diff

It is also possible to define the Lie derivative along a vector at a single point.

Algebraic properties

1. Agreement with other derivatives: .
2. Leibniz rule: .
3. Commutes with contraction: .

Relation to the covariant derivative

For any affine connexion , we have

#state/develop | #lang/en | #SemBr