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Hawking and ellis help

  1. Dec 23, 2009 #1
    I'm reading Hawking and Ellis, and on p.16 they say that

    "The subspace of [tex]T_p[/tex] defined by [tex]\langle \omega,x \rangle[/tex]=(constant) for a given one-form [tex]\omega[/tex], is linear."

    But in what sense is this true? For if the constant is non-zero, the 0 of [tex]T_p[/tex] is not in the subspace, nor does it satisfy the usual linearity condition.

    By analogy with euclidean space, the points [tex]r \cdot a = d[/tex] form a plane, but not technically a subspace of the original space (since it is "shifted"). Am I missing something?
  2. jcsd
  3. Dec 24, 2009 #2

    George Jones

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    No, I don't think that you are missing anything, especially considering the sentence that follows the sentence which you quoted.
  4. Dec 24, 2009 #3

    Turns out that's the least of my difficulties in this book, but it's quite interesting.
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