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 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

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. 
@article{SM_1989_64_2_a17,
     author = {V. T. Fomenko and I. A. Bikchantaev},
     title = {Application of generalized analytic functions on {Riemann} surfaces to the investigation of $G$-deformations of two-dimensional surfaces in~$E^4$},
     journal = {Sbornik. Mathematics},
     pages = {557--569},
     year = {1989},
     volume = {64},
     number = {2},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1989_64_2_a17/}
}
TY  - JOUR
AU  - V. T. Fomenko
AU  - I. A. Bikchantaev
TI  - Application of generalized analytic functions on Riemann surfaces to the investigation of $G$-deformations of two-dimensional surfaces in $E^4$
JO  - Sbornik. Mathematics
PY  - 1989
SP  - 557
EP  - 569
VL  - 64
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/SM_1989_64_2_a17/
LA  - en
ID  - SM_1989_64_2_a17
ER  - 
%0 Journal Article
%A V. T. Fomenko
%A I. A. Bikchantaev
%T Application of generalized analytic functions on Riemann surfaces to the investigation of $G$-deformations of two-dimensional surfaces in $E^4$
%J Sbornik. Mathematics
%D 1989
%P 557-569
%V 64
%N 2
%U http://geodesic.mathdoc.fr/item/SM_1989_64_2_a17/
%G en
%F SM_1989_64_2_a17
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/

[1] Vekua I. N., Obobschennye analiticheskie funktsii, FM, M., 1959 | MR

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

[3] Fomenko V. T., “Nekotorye svoistva dvumernykh poverkhnostei s nulevym normalnym krucheniem”, Matem. sb., 106(148) (1978), 589–603 | MR | Zbl

[4] Gunning R. C, Narasimhan R., “Immersion of open Riemann surfaces”, Math. Ann., 174:2 (1967), 103–108 | DOI | MR | Zbl

[5] Kusunoki Y., “Characterizations of canonical differentials”, J. Math. Kyoto Univ., 5:3 (1966), 197–207 | MR | Zbl

[6] Bikchantaev I. A., “Teorema Liuvillya dlya obobschennykh analiticheskikh funktsii na otkrytoi rimanovoi poverkhnosti”, Izv. vuzov. Matematika, 1983, no. 3, 12–16 | MR | Zbl

[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