Application of generalized analytic functions on Riemann surfaces to the investigation of $G$-deformations of two-dimensional surfaces in $E^4$

Deformations of two-dimensional surfaces in four-dimensional Euclidean space preserving their Grassmannian image ($G$-deformations) are investigated. The surfaces are assumed to belong to a certain subclass of the class of surfaces of negative Gaussian curvature. Conditions are obtained for the existence of $G$-deformations having constricted points and subject to a condition of generalized sliding; the number of linearly independent $G$-deformations satisfying these conditions is found. In obtaining these results, properties of generalized analytic functions on Riemann surfaces are used. In particular, formulas are established for defect numbers for the Hilbert boundary problem for generalized analytic functions on a compact Riemann surface with boundary.
Bibliography: 8 titles.