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Let omega=x dx+y dy+z dz be a 1-form

  1. Apr 1, 2005 #1
    Here an excercise I found between old exams:
    Let omega=x dx+y dy+z dz be a 1-form on R^3 and X=(x,y,z) a vectorfield.
    Compute L_X(omega) as derivative of the pullback of omega under the flow generated by X.
    I think the flow generated by X is (e^t,e^t,e^t), but I don't know how to proceed (computing the pullback, inserting omega en differentating at t=0.
    Anyone? :smile:
     
  2. jcsd
  3. Aug 19, 2009 #2

    Reb

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    Re: Lie-derivative



    Apply Cartan's formula: [tex]L_X(\omega)=i_X d\omega+d(i_X\omega)[/tex], [tex]d\omega[/tex] being the exterior derivative and [tex]i_X(\omega)[/tex] the antiderivation.
     
  4. Aug 19, 2009 #3

    George Jones

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    Re: Lie-derivative

    While this is a nice answer, the thread is over four years old, and it has been more than two years since the original poster lat signed in.
     
  5. Aug 19, 2009 #4

    Reb

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    Re: Lie-derivative


    Yeap, I guess Carbis won't be needing it for his homework anymore.


    Anyhow, I enjoy digging up interesting questions that no-one ever bothered to answer...
    It's something like dating a middle-aged virgin.
    (Will this get me banned? damn...:yuck:)
     
  6. Aug 19, 2009 #5
    Re: Lie-derivative

    I think answering old questions is good because when someone Googles the question, then they'll be more likely to find the answer.
     
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