commuting vector fields
If is a subset of , then we say that vector fields and commute on if they commute at every pont of . In the case where , i.e. when the vector fields commute at every point of the manifold, then we simply say that and are commute.
A set of vector fields on a manifold is said to be commuting on a set if, for every pair of vector fields and , it is the case that and commute.
If is an open set and is a set of commuting vector fields on , then the cardinality of is not greater than the dimension of the manifold and one can find a local coordinate system about any point of for which these vector fields are coordinate vector fields.
|Title||commuting vector fields|
|Date of creation||2013-03-22 15:22:37|
|Last modified on||2013-03-22 15:22:37|
|Last modified by||matte (1858)|