Corollary of Leibniz rule for Lie bracket

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Revision as of 01:02, 5 April 2008 by Vipul (talk | contribs) (New page: ==Statement== This is an identity that uses the Leibniz rule to measure the failure of the Lie bracket operation from being <math>C^\infty</math>-linear. Let <math>X,Y</math> be smooth [...)
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Statement

This is an identity that uses the Leibniz rule to measure the failure of the Lie bracket operation from being C^\infty-linear.

Let X,Y be smooth vector fields on a differential manifold M and f be in C^\infty(M). We then have:

f[X,Y] = [fX,Y] + (Yf)X