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We consider Riemannian 4-manifolds $(X,g_X)$ with a Spin^c-structure and asuitable circle bundle $Y$ over $X$ such that the Spin^c-structure on $X$ liftsto a spin structure on $Y$. With respect to these structures a spinor $\phi$ on$X$ lifts to an untwisted spinor $\psi$ on $Y$ and a U(1)-gauge field $A$ forthe Spin^c-structure can be absorbed into a Kaluza-Klein metric $g_Y^A$ on $Y$.We show that irreducible solutions $(A,\phi)$ to the Seiberg-Witten equationson $(X,g_X)$ for the given Spin^c-structure are equivalent to irreduciblesolutions $\psi$ of a Dirac equation with cubic non-linearity on theKaluza-Klein circle bundle $(Y,g_Y^A)$. As an application we consider solutionsto the equations in the case of Sasaki 5-manifolds which are circle bundlesover Kaehler-Einstein surfaces.

A lift of the Seiberg-Witten equations to Kaluza-Klein 5-manifolds