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.
Symplectic Pairs and Intrinsically Harmonic Forms
Bande, G
Primo
2023-01-01
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.
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