An example of isometric immersion of a domain of 3-dimensional Lobachevsky space into $E^6$ with a section as the Veronese surface

Some example of isometric immersion of a domain of the Lobachevsky space $L^3$ into $E^6$ is constructed in such a way that every intersection of the obtained submanifold with coordinate hyperplane $x^6=const$ be the Veronese surface. The submanifold is not orientable and admits a $2$-parametric family of motions along itself. It is also proved general statements on existence of immersions of some domain of $L^3$ into $E^k$, $k>5$, in the form of special submanifolds.