Bianchi surfaces in R3 and deformation of hyperelliptic curves

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.Translated from Matematicheskie Zametki, Vol. 52, No. 3, pp. 78–88, September, 1992.The first author (D. A. K.) wishes to express his appreciation to A. I. Bobenko for useful discussion.