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Parallel transport

  1. Oct 22, 2004 #1
    hi,
    i am trying to show that the amount by which a vector is rotated by parallel transport around a triangle whose sides are arcs of great circles equals the excess of the sum of the angles over 180 degrees.

    this is what i have found out so far
    call the angles of the triangle (assuming locally flat space) a, b and c.
    then
    [tex]a+b+c=\pi +\frac{1}{R^2} Area(T)[/tex]

    where Area(T) is the area of the triangle.

    this is as far as i can get, i have looked up a few places on parallel transport but the notation used to explain it is very nasty...which is a bit over kill for which i believe to be a much easier problem than it looks.

    pls help
     
  2. jcsd
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