This article is cited in 4 scientific papers (total in 4 papers)
Application of generalized analytic functions on Riemann surfaces to the investigation of $G$-deformations of two-dimensional surfaces in $E^4$
V. T. Fomenko, I. A. Bikchantaev
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.
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Mathematics of the USSR-Sbornik, 1989, 64:2, 557–569
MSC: Primary 30G20, 30F99, 53A05; Secondary 30F30, 30E25, 35J55
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 $E^4$”, Mat. Sb. (N.S.), 136(178):4(8) (1988), 561–573; Math. USSR-Sb., 64:2 (1989), 557–569
Citation in format AMSBIB
\by V.~T.~Fomenko, I.~A.~Bikchantaev
\paper Application of generalized analytic functions on Riemann surfaces to the investigation of $G$-deformations of two-dimensional surfaces in~$E^4$
\jour Mat. Sb. (N.S.)
\jour Math. USSR-Sb.
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A. A. Borisenko, Yu. A. Nikolaevskii, “Grassmann manifolds and the Grassmann image of submanifolds”, Russian Math. Surveys, 46:2 (1991), 45–94
Bikchantaev I., “The Hilbert Problem for First-Order Linear Elliptic Systems on a Riemann Surface with Boundary”, Differ. Equ., 36:4 (2000), 559–566
I. A. Bikchantaev, “The Hilbert problem for a first-order linear elliptic system with noncompactly supported coefficients on a Riemann surface with a boundary”, Russian Math. (Iz. VUZ), 50:1 (2006), 14–22
D. A. Zhukov, “Beskonechno malye MG-deformatsii ovaloida”, Vladikavk. matem. zhurn., 15:2 (2013), 35–44
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