Involutivity of distributions at points of superdense tangency with respect to normal currents

Abstract

Let${\mathcal {D}}$and$T$be, respectively, a$C^1$distribution of$k$-planes and a normal$k$-current on${\mathbb {R}}^n$. Then${\mathcal {D}}$has to be involutive at almost every superdensity point of the tangency set of$T$with respect to${\mathcal {D}}$.