# zbMATH — the first resource for mathematics

A complex of differential forms on contact manifolds. (Un complexe de formes différentielles sur les variétés de contact.) (French) Zbl 0694.57010
If $$M^{2n+1}$$ is a contact manifold, the author constructs a complex of differential forms “modulo contact forms”, whose cohomology coincides with the de Rham cohomology of $$M$$. If the contact distribution $$Q$$ possesses an integrable strictly pseudoconvex CR structure and $$n>1$$, then modulo an assumption on the associated pseudohermitian curvature tensor, the first Betti number of $$M$$ vanishes. Unfortunately this result does not extend to dimension three.
Reviewer: C. Thomas

##### MSC:
 57R15 Specialized structures on manifolds (spin manifolds, framed manifolds, etc.) 58A12 de Rham theory in global analysis 53D10 Contact manifolds (general theory) 53C15 General geometric structures on manifolds (almost complex, almost product structures, etc.) 57R19 Algebraic topology on manifolds and differential topology