Certain multidimensional two-webs of the type $T_{m,n}^{mn}$

Multidimensional 2-webs are formed by two families of submanifolds $V_m$ and $V_n$ of a given $(m+n+p)$-manifold $\mathfrak M$ so that through every point of $V_{mn}$ passes exactly one submanifold of each family. 2-webs with some prescribed differential-geometric properties are constructed.