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We draw connections between contact topology and the study of Maxwell fieldsin vacuo on 3-dimensional closed Riemannian manifolds in 4-dimensionalLorentzian manifolds. This is accomplished by showing that contact topologicalmethods can be applied to reveal topological features of a class of solutionsto Maxwell's equations. This class of Maxwell fields is such that electricfields are parallel to magnetic fields. In addition these electromagneticfields are composed of the so-called Beltrami fields. We employ severaltheorems resolving the Weinstein conjecture on closed manifolds with contactstructures and stable Hamiltonian structures, where this conjecture refers tothe existence of periodic orbits of the Reeb vector fields. Here a contact formis a special case of a stable Hamiltonian structure. After showing how torelate Reeb vector fields with electromagnetic 1-forms, we apply a theoremregarding contact manifolds and an improved theorem regarding stableHamiltonian structures. Then a closed field line is shown to exist, where fieldlines are generated by Maxwell fields at an instant time. In addition,electromagnetic energies are shown to be conserved along the Reeb vectorfields.

Contact topology and electromagnetism: the Weinstein conjecture and Beltrami-Maxwell fields