I am interested in the Heisenberg manifold, which is the quotient of the real Heisenberg group by the discrete Heisenberg (sub)group. It is a 3 -manifold which may be viewed as a circle bundle over the 2 -torus, or as a 2 -torus bundle over the circle. i know that all principal fiber bundles have a connection form,then can we find a connection form(ehresmann)form?sincerrely ,thanks.
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