Geodesic
Isometric immersions of a Euclidean plane in Lobachevskii space
Matematičeskie zametki, Tome 10 (1971) no. 3, pp. 327-332.

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It is proved that any regular isometric immersion of a Euclidean plane in (three-dimensional) Lobachevskii space is either a homeomorphism onto an orisphere or a covering of the surface formed by the rotation of an equidistant about its base. 
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     author = {Yu. A. Volkov and S. M. Vladimirova},
     title = {Isometric immersions of a {Euclidean} plane in {Lobachevskii} space},
     journal = {Matemati\v{c}eskie zametki},
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     year = {1971},
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Yu. A. Volkov; S. M. Vladimirova. Isometric immersions of a Euclidean plane in Lobachevskii space. Matematičeskie zametki, Tome 10 (1971) no. 3, pp. 327-332. http://geodesic.mathdoc.fr/item/MZM_1971_10_3_a10/