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Tensor Field

  1. Oct 2, 2007 #1
    I have a following problem.

    Let D be an operator taking the C^oo functions F to F, and the C^oo vector fields V to V, such that D:F-->F and
    D:V-->V, are linear over R(real) and
    D(f Y) = f * DY+Df * Y. Here * is a multiplication

    Show that D has a unique extension to an operator taking tensor fields of type(k, l) to themselves such that
    (1) D is linear over R(real).
    (2) D(A $ B)= DA $ B+ A $ DB. Here $ is a tensor product.
    (3) for any contraction C, DC=CD.

    If you have Spivak's geometry book. This is a problem 5-15.

    Any help would be appreciated.
    Thanks.
     
  2. jcsd
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