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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

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# Homework Help: Parallel transport

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