Geodesic
Reconstruction of 3-submanifolds of large codimension in Euclidean spaces from their Gauss image
Matematičeskie zametki, Tome 62 (1997) no. 5, pp. 694-699

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We present necessary and sufficient conditions for a regular three-dimensional manifold in the Grassmannian manifold $G(m,m+3)$ to be the Gauss image of a regular 3-submanifold in $(m+3)$-dimensional Euclidean space for $m>4$. 
@article{MZM_1997_62_5_a6,
     author = {V. A. Gorkavyy},
     title = {Reconstruction of 3-submanifolds of large codimension in {Euclidean} spaces from their {Gauss} image},
     journal = {Matemati\v{c}eskie zametki},
     pages = {694--699},
     publisher = {mathdoc},
     volume = {62},
     number = {5},
     year = {1997},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1997_62_5_a6/}
}
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%F MZM_1997_62_5_a6
V. A. Gorkavyy. Reconstruction of 3-submanifolds of large codimension in Euclidean spaces from their Gauss image. Matematičeskie zametki, Tome 62 (1997) no. 5, pp. 694-699. http://geodesic.mathdoc.fr/item/MZM_1997_62_5_a6/