Geodesic
On regular embedding integrally in $R^3$ of metrics of class $C^4$ of negative curvature
Matematičeskie zametki, Tome 14 (1973) no. 2, pp. 261-266 
E. V. Shikin. On regular embedding integrally in $R^3$ of metrics of class $C^4$ of negative curvature. Matematičeskie zametki, Tome 14 (1973) no. 2, pp. 261-266. http://geodesic.mathdoc.fr/item/MZM_1973_14_2_a11/
@article{MZM_1973_14_2_a11,
     author = {E. V. Shikin},
     title = {On regular embedding integrally in $R^3$ of metrics of class $C^4$ of negative curvature},
     journal = {Matemati\v{c}eskie zametki},
     pages = {261--266},
     year = {1973},
     volume = {14},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1973_14_2_a11/}
}
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%G ru
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Voir la notice de l'article provenant de la source Math-Net.Ru

On the $x_0y$ plane let there be specified a complete metric of negative curvature $K$ by means of the line element $$ds^2=dx^2+B^2(x,y)\,dy^2$$, and, in the strip $\Pi_a=\{0\le x\le a,-\infty, let the following conditions be met: $B(x,y)$ is a $C^4$-bounded function $B\ge\lambda>0$, $K\le-\mu^2<0$ ($\lambda$ and $\mu$ are constants). Then, the metric in strip $\Pi_a$ is embedded in $R^3$ by means of a surface of class C3.