Almost complex structures and calibrated integral cycles in contact 5-manifolds

In a contact manifold (M^5, alpha), we consider almost complex structures J which satisfy, for any vector v in the horizontal distribution, d alpha (v,Jv) = 0. We prove that integral cycles whose approximate tangent planes have the property of being J-invariant are in fact smooth Legendrian curves except possibly at isolated points and we investigate how such structures J are related to calibrations.