On construction of isometric immersions of the domains of Lobachevsky plane $L^2$ into $E^4$ by using solutions of the “sine-Gordon” equation

Isometric immersions of the Lobachevsky plane $L^2$ into $E^4$, are considered. These immersions are surfaces in $E^4$, which have a vanishing Gaussian torsion. The immersions are constructed by using different solutions of the “sine-Gordon” equation. It is proved that the domains of $L^2$, which are immersed, are parts of the domains bounded by two horocycles or two equidistants. The sizes of the domains under consideration are estimated.