English

Commutators of flows and fields

Differential Geometry 2009-09-25 v1

Abstract

The well known formula [X,Y]=122t20(\FltY\o\FltX\o\FltY\o\FltX)[X,Y]=\tfrac12\tfrac{\partial^2}{\partial t^2}|_0 (\Fl^Y_{-t}\o\Fl^X_{-t}\o\Fl^Y_t\o\Fl^X_t) for vector fields XX, YY is generalized to arbitrary bracket expressions and arbitrary curves of local diffeomorphisms.

Keywords

Cite

@article{arxiv.math/9204221,
  title  = {Commutators of flows and fields},
  author = {Markus Mauhart and Peter W. Michor},
  journal= {arXiv preprint arXiv:math/9204221},
  year   = {2009}
}