Seiberg-Witten Like equations on 5-dimensional contact metric manifolds

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In this paper, we write down Seiberg-Witten equations on contact metric manifolds of dimension 5. Any contact metric manifold has a spinᶜ structure. For Dirac equation we use Dirac type operators associated to the generalized Tanaka-Webster connection on spinᶜ spinor bundle of a contact metric manifold. For curvature equation we need to self-duality concept. Self-duality concept is significant on odd dimensional manifolds, particularly, on 5-dimensional contact manifolds. Finally, we give a global solution to these equations on strictly pseudoconvex CR manifolds.