I am having trouble visualizing when a 2 form is exact and have a specific case that I am struggling with at the moment. Any help is welcome.(adsbygoogle = window.adsbygoogle || []).push({});

Take an oriented 2 torus and divide it ,using parallel circles, into an even number of tube shaped regions.

In each tube, assign a 2-form that fades to zero at its bounding circles and require the following:

- these two forms fit together along the tube boundaries to give a global 2 form

- Each form has the opposite orientation from the 2 forms in its adjacent regions

- The integral of the induced global 2 form is zero.

- None of the forms are identically zero in any tube.

This form is exact. But how do I picture the one form that it is the exterior derivative of?

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# Exact forms on the 2 torus

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