Geodesic
Bianchi surfaces in $\mathbf{R}^3$ and deformation of hyperelliptic curves
Matematičeskie zametki, Tome 52 (1992) no. 3, pp. 78-88.

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New solutions of the problem of describing hyperbolic surfaces of specified negative Gaussian curvature are obtained. The answer is given in terms of 9 functions. 
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     author = {D. A. Korotkin and V. A. Reznik},
     title = {Bianchi surfaces in $\mathbf{R}^3$ and deformation of hyperelliptic curves},
     journal = {Matemati\v{c}eskie zametki},
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     year = {1992},
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D. A. Korotkin; V. A. Reznik. Bianchi surfaces in $\mathbf{R}^3$ and deformation of hyperelliptic curves. Matematičeskie zametki, Tome 52 (1992) no. 3, pp. 78-88. http://geodesic.mathdoc.fr/item/MZM_1992_52_3_a7/