On toroidal submanifolds of constant negative curvature

Earlier M. L. Rabelo and K. Tenenblat have introduced the notion of toroidal submanifolds generated by some curve $\alpha$ and they have constructed immersions of domains of the $n$-dimensional Lobachevsky space $L^n$ in $E^{2n-1}$ as toroidal submanifolds. Here these submanifolds are reconstructed by a simply way, and in the case $n=3$ the influence of the torsion $k$ of the curve $\alpha$ on the geometry of the submanifolds $M^3\subset E^5$ is investigated. Here the torsion appears in the coefficient of torsion of the special normal basis of $M^3$. The Grassmann image of its has been constructed.