Odd dimensional tori are contact manifolds

Frédéric Bourgeois (1)

1 Department of Mathematics [Stanford]

We show that, for every contact manifold $M$ and for every Riemann surface $\Sigma$ of genus at least 1, the manifold $\Sigma \times M$ admits a contact structure. In particular, the tori $T^{2n+1}$ are contact manifolds.

Domaines: Géométrie symplectique [math.SG]

Frédéric Bourgeois. Odd dimensional tori are contact manifolds. International Mathematics Research Notices, 2002, 2002 (30), pp.1571-1574. ⟨10.1155/S1073792802205048⟩. ⟨hal-01011013⟩