MG-deformations of a surface of positive Gaussian curvature under assignment of variation of any tensor along an edge

We investigate the infinitesimal MG-deformations of a simply connected surface with positive Gaussian curvature. We choose any symmetric tensor on the surface, variation of the first and the second invariant of this tensor equals given function along a boundary. The study of this boundary-value problems is reduced to the investigation of a solvability of Riemann–Gilbert boundary-value problem and to calculation of its index. As a result we get theorems of existence and uniqness for the infinitesimal MG-deformation.