Contact-pair neighborhood theorem for submanifolds in symplectic pairs

Abstract

Let M be a 2n-dimensional smooth manifold associated with the structure of symplectic pair which is a pair of closed 2-forms of constant ranks with complementary kernel foliations. Let Q ⊂ M be a codimension 2 compact submanifold. We show some sufficient and necessary conditions on the existence of the structure of contact pair (α, β) on Q, which is a pair of 1-forms of constant classes whose characteristic foliations are transverse and complementary such that α and β restrict to contact forms on the leaves of the characteristic foliations of β and α, respectively. This is a generalization of the neighborhood theorem for contact-type hypersurfaces in symplectic topology.