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On extension of a restriction of a symplectic form. (Russian) Zbl 0853.53029

The author examines the problem of an extension of a given closed 2-form \(\tau\) of rank \(2n-2\) on a compact orientable \(2n-1\) manifold \(Q\) to a symplectic form \(\omega \) on \(Q\times (-\varepsilon, \varepsilon)\). The author proves that the extension \(\omega\) of \(\tau\) always exists. He classifies the forms \(\omega\) up to a “homotopy” (then there are two different extensions) and up to a “diffeomorphism” (then there is a unique extension).

MSC:

53C15 General geometric structures on manifolds (almost complex, almost product structures, etc.)
58A10 Differential forms in global analysis
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