Lie derivative
Let be a smooth manifold, a vector field on , and a tensor on . Then the Lie derivative of along is a tensor of the same rank as defined as
where is the flow of , and is pullback by .
The Lie derivative is a notion of directional derivative for tensors. Intuitively, this is the change in in the direction of .
If and are vector fields, then , the standard Lie bracket of vector fields.
Title | Lie derivative |
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Canonical name | LieDerivative |
Date of creation | 2013-03-22 13:14:10 |
Last modified on | 2013-03-22 13:14:10 |
Owner | rspuzio (6075) |
Last modified by | rspuzio (6075) |
Numerical id | 6 |
Author | rspuzio (6075) |
Entry type | Definition |
Classification | msc 53-00 |
Related topic | LeibnizNotationForVectorFields |
Related topic | CartanCalculus |