Symplectic Pairs and Intrinsically Harmonic Forms

Abstract

In this short note, we prove two properties of symplectic pairs on a four-manifold: firstly we prove that two transversal orientable foliations of codimension two, which are taut for the same Riemannian metric, are the characteristic foliations of a symplectic pair; secondly, we characterize intrinsically harmonic 2-forms of rank two as part of a symplectic pair.

Keywords

• symplectic pairs
• taut foliations
• intrinsically harmonic forms