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Lie brackets and differential

  1. May 20, 2010 #1
    I have an isometry between two manifolds M and N. Can someone help me why the following is true

    DF([X,Y])=[DF(X),DF(Y)], where X,Y are vector fields on M.

  2. jcsd
  3. May 22, 2010 #2


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    Is the isometry called F or DF? Do you mean dF? How is your D defined?
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