On neighborhood theorems for symplectic pairs

Abstract

Let M be a 2n-dimensional smooth manifold. We study local properties for a symplectic pair on M which is a pair of closed 2-forms of constant ranks with complementary kernel foliations. We show that some neighborhood theorems for submanifolds of M and Darboux type theorem hold. For more general case of recursion operators intertwining a pair of symplectic forms, we also prove that some neighborhood theorem holds.