Geodesic
Isometric immersions of domains of Lobachevsky space in Euclidean spaces
Zapiski Nauchnykh Seminarov POMI, Differential geometry, Lie groups and mechanics. Part 15–1, Tome 234 (1996), pp. 11-16

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Immersions of domains of the $n$-dimensional Lobachevsky space $L^n$ in the $(2n-1)$-dimensional Euclidean space $E^{2n-1}$ are studied. It is shown that the problem of isometric immersion of domains of $L^n$ in $E^{2n-1}$ is reduced to the study of a certain system of nonlinear partial differential equations, yielding the sine-Gordon equation as one of the special cases. 
@article{ZNSL_1996_234_a2,
     author = {Yu. A. Aminov},
     title = {Isometric immersions of domains of {Lobachevsky} space in {Euclidean} spaces},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {11--16},
     publisher = {mathdoc},
     volume = {234},
     year = {1996},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1996_234_a2/}
}
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Yu. A. Aminov. Isometric immersions of domains of Lobachevsky space in Euclidean spaces. Zapiski Nauchnykh Seminarov POMI, Differential geometry, Lie groups and mechanics. Part 15–1, Tome 234 (1996), pp. 11-16. http://geodesic.mathdoc.fr/item/ZNSL_1996_234_a2/