Geodesic
Application of generalized analytic functions on Riemann surfaces to the investigation of $G$-deformations of two-dimensional surfaces in $E^4$
Sbornik. Mathematics, Tome 64 (1989) no. 2, pp. 557-569 
V. T. Fomenko; I. A. Bikchantaev. Application of generalized analytic functions on Riemann surfaces to the investigation of $G$-deformations of two-dimensional surfaces in $E^4$. Sbornik. Mathematics, Tome 64 (1989) no. 2, pp. 557-569. http://geodesic.mathdoc.fr/item/SM_1989_64_2_a17/
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     title = {Application of generalized analytic functions on {Riemann} surfaces to the investigation of $G$-deformations of two-dimensional surfaces in~$E^4$},
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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.

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[2] Eizenkhart L. P., Rimanova geometriya, IL, M., 1948

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[7] Gakhov F. D., Zverovich E. I., Samko S. G., “Priraschenie argumenta, logarifmicheskii vychet i obobschennyi printsip argumenta”, DAN SSSR, 215:3 (1974), 432–435

[8] Bikchantaev I. A., “Integralnye predstavleniya reshenii ellipticheskikh sistem pervogo poryadka na rimanovykh poverkhnostyakh”, Differents. uravneniya, 22:9 (1986), 1557–1565 | MR | Zbl