Решение проблемы Гронвелла об эквивалентности грассмановых тканей

Let $GW$ and $GW$ be two equivalent Grassmannian three-webs, formed by the leaves of dimension $r$, and $arphi$ be a local diffeomorphism which maps the foliations of $GW$ onto the foliations of $GW$. Then, $arphi$ is a projective transformation. It follows from that the positive solution of the Gronwell problem in case $r>1$: let $W$ be a grassmannizable three-web, $arphi$ and $$ be local diffeomorphisms mapping the web $W$ onto a Grassmannian three-web, then $arphi ^-1$ is a projective transformation. In case $r=1$ the Gronwell problem has a positive solution for non-regular webs. A Grassmannian three-web $GW$ which is equivalent to the given regular Grassmannian 3-web $GW$, together with the corresponding local diffeomorphism $arphi$, exists with the arbitrariness of 12 constants.