This article is cited in 4 papers

Defining a surface in 4-dimensional Euclidean space by means of its Grassmann image

Yu. A. Aminov


Abstract: 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.

UDC: 513.7

MSC: Primary 53A05; Secondary 14M15

Received: 10.11.1980

 English version: Mathematics of the USSR-Sbornik, 1983, 45:2, 155–168

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