Almost complex structures for symplectic pairs

Let M be a 2n-dimensional smooth manifold with a linear symplectic pair (omega, tau) which is a pair of skew-symmetric 2-forms of constant ranks with complementary kernel foliations. We study properties of almost complex structures compatible with the symplectic pair on M. We show that the space of compatible almost complex structures is contractible. This generalizes a result on compatible almost complex structures for symplectic manifolds. (C) 2017 Elsevier B.V. All rights reserved.