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

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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. 
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     author = {Yu. A. Aminov},
     title = {Defining a surface in 4-dimensional {Euclidean} space by means of its {Grassmann} image},
     journal = {Sbornik. Mathematics},
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     volume = {45},
     number = {2},
     year = {1983},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1983_45_2_a0/}
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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/