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I want to find the integral curves of $[X,Y]$, then maybe can use this to prove. Can anyone gives an answer ? Thanks.

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    Is your question the one in the title of this post? Or is it something else?2012-03-13
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    Yes,just the question in the title.2012-03-14
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    Just prove if $X$,$Y$ are both killing vector fields,then $[X,Y]$ is also killing vector field.Can anyone give some suggestions?Thanks.2012-03-14

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