On differential-geometric structures on a manifold of nonholonomic $(n+1)$-web

We consider nonholonomic $(n+1)$-web $NW$ consisting of $n+1$ distributions of codimension $1$ on $n$-dimensional manifold $M$. We prove that an invariant pencil of projective connections exists on the manifold $M$. A unique curvilinear $(n+1)$-web corresponds to the ordered nonholonomic $(n+1)$-web and vice versa. The correspondence is defined by the polarity with respect to an invariant multilinear $n$-form or barycentric subdivision of an $(n+1)$-dimensional simplex. In conclusion we consider nonholonomic $(n+1)$-webs in affine space. The invariant pencil of affine connections is generated by every affine web. We also consider the case when the connections of the pencil are projective.