Geodesic
Geometry of the Grassmann image of a local isometric immersion of Lobachevskii $n$-dimensional isometric immersion of Lobachevskii $n$-dimensional
Sbornik. Mathematics, Tome 188 (1997) no. 1, pp. 1-27 
Yu. A. Aminov. Geometry of the Grassmann image of a local isometric immersion of Lobachevskii $n$-dimensional isometric immersion of Lobachevskii $n$-dimensional. Sbornik. Mathematics, Tome 188 (1997) no. 1, pp. 1-27. http://geodesic.mathdoc.fr/item/SM_1997_188_1_a0/
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Voir la notice de l'article provenant de la source Math-Net.Ru

In this paper we obtain an expression for the curvature tenser of the metric of the Grassmann image of an isometric immersion of Lobachevskii $n$-dimensional space in $(2n-1)$-dimensional Euclidean space. The main result is the following theorem: there is no $C^3$ local isometric immersion of 3-dimensional Lobachevski space in 5-dimensional Euclidean space with constant curvature of the metric of the Grassmann image.

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