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Stability of tangential locally conformal symplectic forms. (English) Zbl 1318.53018

The author defines a tangential Lichnerowicz cohomology on foliated manifolds and shows that on a smooth manifold \(M\) and for a tangentially closed 1-form \(\theta\) on \(M\), the tangential Lichnerowicz cohomology depends only on the tangential cohomology class of \(\theta\). He also proves a version of a de Rham-type theorem for tangential Lichnerowicz cohomology and some results concerning the stability of tangential locally conformal symplectic forms. An interesting example is also presented.

MSC:

53C12 Foliations (differential geometric aspects)
58A12 de Rham theory in global analysis
53D99 Symplectic geometry, contact geometry
57R17 Symplectic and contact topology in high or arbitrary dimension
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