lie bracket of vector fieldsの例文

例文

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1. This can be used to define the Lie bracket of vector fields as follows.
2. The main invariants of an affine connection are its Lie bracket of vector fields can be recovered from the affine connection.
3. The proof of the Jacobi identity follows from because the Lie bracket of vector fields is just their commutator as differential operators.
4. follows from the corresponding identity for the Lie bracket of vector fields, but this is true only up to a locally constant function.
5. Except in locally flat regions, at least some Lie brackets of vector fields from a frame will " not " vanish.