Geodesic
Defining a surface in 4-dimensional Euclidean space by means of its Grassmann image
Sbornik. Mathematics, Tome 45 (1983) no. 2, pp. 155-168 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

In this paper the following problem is solved: if in the Grassmann manifold $G_{2,4}$ a regular submanifold $\Gamma^2$ of dimension 2 is given, does there exist in Euclidean space $E^4$ a regular surface $F^2$ for which $\Gamma^2$ is the Grassmann image? Sufficient conditions are found for this problem to have a solution and for it to be unique. Bibliography: 9 titles. 
@article{SM_1983_45_2_a0,
     author = {Yu. A. Aminov},
     title = {Defining a surface in 4-dimensional {Euclidean} space by means of its {Grassmann} image},
     journal = {Sbornik. Mathematics},
     pages = {155--168},
     year = {1983},
     volume = {45},
     number = {2},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1983_45_2_a0/}
}
TY  - JOUR
AU  - Yu. A. Aminov
TI  - Defining a surface in 4-dimensional Euclidean space by means of its Grassmann image
JO  - Sbornik. Mathematics
PY  - 1983
SP  - 155
EP  - 168
VL  - 45
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/SM_1983_45_2_a0/
LA  - en
ID  - SM_1983_45_2_a0
ER  - 
%0 Journal Article
%A Yu. A. Aminov
%T Defining a surface in 4-dimensional Euclidean space by means of its Grassmann image
%J Sbornik. Mathematics
%D 1983
%P 155-168
%V 45
%N 2
%U http://geodesic.mathdoc.fr/item/SM_1983_45_2_a0/
%G en
%F SM_1983_45_2_a0
Yu. A. Aminov. Defining a surface in 4-dimensional Euclidean space by means of its Grassmann image. Sbornik. Mathematics, Tome 45 (1983) no. 2, pp. 155-168. http://geodesic.mathdoc.fr/item/SM_1983_45_2_a0/

[1] Aminov Yu. A., “O grassmanovom obraze dvumernoi poverkhnosti v chetyrekhmernom evklidovom prostranstve”, Ukr. geom. sb., 1980, no. 23, 3–16 | MR | Zbl

[2] Aminov Yu. A., “Svoistva grassmanova obraza podmnogoobraziya evklidova prostranstva”, Tezisy dokladov na sedmoi vsesoyuznoi konf. po sovr. problemam geometrii, Minsk, 1979, 9

[3] Wong Y.-C., “Sectional curvatures of Grassman manifolds”, Proc. Nat. Acad. Sci. USA, 60:1 (1968), 75–79 | DOI | MR | Zbl

[4] Aminov Yu. A., “O kruchenii dvumernykh poverkhnostei v evklidovykh prostranstvakh”, Ukr. geom. sb., 1975, no. 17, 3–15 | MR | Zbl

[5] Kartan E., Rimanova geometriya v ortogonalnom repere, izd-vo MGU, M., 1960

[6] Shirokov P. A., Tenzornoe ischislenie, izd-vo KGU, Kazan, 1961 | MR

[7] Kurant R., Uravneniya s chastnymi proizvodnymi, Mir, M., 1964 | MR

[8] Lavrentev M. A., “Osnovnaya teorema teorii kvazikonformnykh otobrazhenii ploskikh oblastei”, Izv. AN SSSR, ser. matem., 12 (1948), 513–554 | MR

[9] Polozhii G. N., “Teorema o sokhranenii oblasti dlya nekotorykh ellipticheskikh sistem differentsialnykh uravnenii i ee primeneniya”, Matem. sb., 32(74) (1963), 485–492