Geodesic
On construction of isometric immersions of the domains of Lobachevsky plane $L^2$ into $E^4$
Žurnal matematičeskoj fiziki, analiza, geometrii, Tome 2 (1995) no. 3, pp. 319-328 
O. V. Kuznetsov. On construction of isometric immersions of the domains of Lobachevsky plane $L^2$ into $E^4$. Žurnal matematičeskoj fiziki, analiza, geometrii, Tome 2 (1995) no. 3, pp. 319-328. http://geodesic.mathdoc.fr/item/JMAG_1995_2_3_a5/
@article{JMAG_1995_2_3_a5,
     author = {O. V. Kuznetsov},
     title = {On construction of isometric immersions of the domains of {Lobachevsky} plane $L^2$ into $E^4$},
     journal = {\v{Z}urnal matemati\v{c}eskoj fiziki, analiza, geometrii},
     pages = {319--328},
     year = {1995},
     volume = {2},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/JMAG_1995_2_3_a5/}
}
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Voir la notice de l'article provenant de la source Math-Net.Ru

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.