Geodesic
On the regularity of oricyclic coordinates
Matematičeskie zametki, Tome 17 (1975) no. 3, pp. 475-484 
E. V. Shikin. On the regularity of oricyclic coordinates. Matematičeskie zametki, Tome 17 (1975) no. 3, pp. 475-484. http://geodesic.mathdoc.fr/item/MZM_1975_17_3_a14/
@article{MZM_1975_17_3_a14,
     author = {E. V. Shikin},
     title = {On the regularity of oricyclic coordinates},
     journal = {Matemati\v{c}eskie zametki},
     pages = {475--484},
     year = {1975},
     volume = {17},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1975_17_3_a14/}
}
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Voir la notice de l'article provenant de la source Math-Net.Ru

Suppose there is defined in the plane a complete metric $W^-$, whose curvature $K$ satisfies the inequality $-k_2^2\le K\le -k_1^2$ ($k_1$ and $k_2$ are positive constants) and some regularity hypothesis. Then in the entire domain of definition of the metric $W^-$ one can construct regular oricyclic coordinates $(x,y)$, in which the line element has the form $ds^2=dx^2+B2(x,y)\cdot dy^2$.