Recent content by schulmannerism

  1. S

    Vector Field Commutator Identity in Covariant Derivative

    Whoops I wrote my second post incorrectly, it's editted.
  2. S

    Vector Field Commutator Identity in Covariant Derivative

    Hurkyl -- your (deleted) post was helpful. I see now that I was having trouble with the notation in which a vector times a scalar field denotes the directional derivative in that direction. Then the identity does follow, as you pointed out. Thanks
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    Vector Field Commutator Identity in Covariant Derivative

    Well the original problem is to show that if f(P) is a scalar field such that f(P_0)=1, and A,B,C are vector fields, then [\nabla_A,\nabla_B](f(P)C(P))-[\nabla_A,\nabla_B{A}](C(P))=[\nabla_{[A,B]}(C(P)) Unless I am doing something wrong, this immediately reduces to the above identity, which...
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    Vector Field Commutator Identity in Covariant Derivative

    I am trying to solve an exercise from MTW Gravitation and the following issue has come up: Let D denote uppercase delta (covariant derivative operator) [ _ , _ ] denotes the commutator f is a scalar field, and A and B are vector fields Question: Is it true that [D_A,D_B]f = D_[A,B]f ?
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