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Is this quantity a tensor and why?

  1. Dec 20, 2011 #1
    T[itex]^{jk}[/itex] = [itex]\frac{1}{\sqrt{g}}[/itex][itex]\frac{\partial}{\partial x^{i}}[/itex] ([itex]\sqrt{g}[/itex]B[itex]^{ijk}[/itex])

    Given B[itex]^{ijk}[/itex] is a tensor
    Find if T[itex]^{jk}[/itex] is a tensor and explain why and if not what can be done to
    B[itex]^{ijk}[/itex] to make T[itex]^{jk}[/itex] a tensor ?

    I tried to solve this but i think i'am missing some rules !!!

    I think T[itex]^{jk}[/itex] looks like a div of B = B[itex]^{ijk}[/itex],i
    i tried to substitute B[itex]^{ijk}[/itex],i with the derivative but i end up with a big quantity with christoffel symbols

    any help plz!!
     
  2. jcsd
  3. Dec 20, 2011 #2

    dextercioby

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    It's the divergence of a rank 3 (0,3) tensor which is a contraction from the covariant derivative of a tensor. Through contraction, the tensor/pseudo-tensor character is preserved, so...
     
  4. Dec 23, 2011 #3
    thank you for the reply.
    I found this and i guess it is your answer!

    The divergence of a given contravariant tensor
    results from the expression of the covariant
    derivative of that tensor, and due to the contraction,
    the divergence will be a tensor of a rank less by two
    units.
     
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