Closed forms on symplectic fibre bundles (Q791891)

The paper deals with the problem of finding a closed extension of a symplectic structure along the fibres of a fibre bundle. A necessary and sufficient condition \((H^{2k}\) (fibre, \({\mathbb{R}})=0\) for at least one k) is given. A very nice interpretation of this result in terms of principal connections is given. The result is also interpreted in the language of geometric quantization.