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The Einstein field equations can be derived in $n$ dimensions ($n>2$) by thevariations of the Palatini action. The Killing reduction of 5-dimensionalPalatini action is studied on the assumption that pentads and Lorentzconnections are preserved by the Killing vector field. A Palatini formalism of4-dimensional action for gravity coupled to a vector field and a scalar fieldis obtained, which gives exactly the same fields equations in Kaluza-Kleintheory.Comment: 10 page

PALATINI FORMALISM OF FIVE-DIMENSIONAL KALUZA–KLEIN THEORY