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Abstract
In this paper we consider first-order infinitesimal deformations of simply connected regular surfaces in three-dimensional Euclidean space with a stationary Ricci tensor. The search for the vector field of this deformation in the general case is reduced to the study and solution of a system of seven equations, including differential equations, with respect to seven unknown functions. It is proved that every regular surface of non-zero Gaussian and mean curvatures admits a first-order nonlinear deformation with a stationary Ricci tensor. The methods of tensor analysis, the theory of differential equations and their boundary value problems are used to solve the stated problems.
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