There are 2 great circles C1 and C2 on a sphere and they are at an angle of [itex] \alpha [/itex] with each other at the north pole. Form a closed path from the north pole along C1 to the equator, then along the equator to C2, and back up along C2 to the north pole. Show that the holonomy is also the angle [itex] \alpha [/itex].(adsbygoogle = window.adsbygoogle || []).push({});

my book talks about finding the holonomy along a curve and give the simple formula [itex] \theta(t) = \theta(0) - \int \omega_{21} dt [/itex] where [itex] \omega_{21} [/itex] is given by [itex] \nabla_{v} \frac{x_u}{sqrt{E}} = \omega_{21} \frac{x_v}{sqrt{G}} [/itex].

The problem is that along each piece of the path, C1, C2, and the equator, the holonomy is 0 along each individually, but when put together to form the closed path described above, there is obviously a nonzero holonomy. how do i calculate the holonomy along this path which is made up of 3 different curves? i've tried to find a parametrization for the closed path but could not think of one. can someone help guide me along in this problem?

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# Homework Help: Calculating the holonomy on a sphere

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