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Math Help - vanishing measure of a manifold with codimension 2

  1. #1
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    vanishing measure of a manifold with codimension 2

    Hey everyone,
    I am reading a paper by Claude LeBrun, which I have been discussing with several of my classmates but we cannot seem to explain a fact he uses: A codimension 2 submanifold B of the complex plane CP_2 has zero measure when you integrate something on it. I believe this is general statement, but really what we are concerned with is determining the first Chern class, so we are integrating functions of curvature 2-forms.

    I have been trying to explain why this works using some theorems of exterior algebra and Hodge duality (since a∧*b=<a,b>du for measure du) but I haven't really gotten anywhere. Any insight would be appreciated.
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  2. #2
    Super Member Rebesques's Avatar
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    has zero measure when you integrate something on it.
    Please re-state...
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