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In this note we announce some results, due to appear in , , on the structure of integral and normal currents, and their relation to Frobenius theorem. In particular we show that an integral current cannot be tangent to a distribution of planes which is nowhere involutive (Theorem 3.6), and that a normal current which is tangent to an involutive distribution of planes can be locally foliated in terms of integral currents (Theorem 4.3). This statement gives a partial answer to a questiondoi:10.4171/rlm/788 fatcat:5ajzrktdxjaj3edyslt74yd3uu