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Author finds the solutions of the Christoffel problem for open and closedsurfaces in Riemannian space. The Christoffel problem is reduced to the problemof construction the continuous G-deformations preserving the sum of principalradii of curvature for every point of surface in Riemannian space.G-deformation transfers every normal vector of surface in parallel along thepath of the translation for each point of surface. The following analogs of theMinkowski problem for open and closed surfaces in Riemannian space are beingconsidered in this article: 1) the problem of construction the surface withprescribed mean curvature and condition of G-deformation; 2) the problem ofconstruction the deformations preserving the area of each arbitrary region ofsurface and condition of G-deformation.

The Christoffel problem and two analogs of the Minkowski problem in Riemannian space