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

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.
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