BRACKET AND EXPONENTIAL FOR A NEW TYPE OF VECTOR FIELD
Technical rept. no. 17
WASHINGTON UNIV SEATTLE
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Robert Hermann introduced the concept of tangent vector fields on the space of functions from one manifold to another. He applied these to give a new proof of the Cartan-Kahler theorem. An example of such vector fields are maps from the jet space to the tangent bundle of the target space which commute with projections. It is this class of vector fields which we study here. Using prolongations a Lie bracket operation is defined and justified on the grounds that it agrees with the primitive definition when the latter has meaning here. By similar methods an exponential expansion is deduced. An example is given which shows that the 1-parameter transformation groups on the function space cannot be considered a parameter space for a pseudo group in Kuranishis sense, for it need not involve infinite analytic mappings.
- Theoretical Mathematics