Geodesic
The analogue of the Grassmannian image for submanifolds of a sphere
Sbornik. Mathematics, Tome 187 (1996) no. 9, pp. 1283-1300 Cet article a éte moissonné depuis la source Math-Net.Ru

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We study the analogue of the Grassmannian image for submanifolds of a sphere, as described by Obata, and investigate the problem of reconstructing a submanifold from its Grassmannian image. 
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V. A. Gorkavyy. The analogue of the Grassmannian image for submanifolds of a sphere. Sbornik. Mathematics, Tome 187 (1996) no. 9, pp. 1283-1300. http://geodesic.mathdoc.fr/item/SM_1996_187_9_a1/

[1] Obata, “The Gauss map of immersion of Riemannian manifolds in spaces of constant curvature”, J. Differential Geom., 2:2 (1968), 217–223 | MR | Zbl

[2] Borisenko A. A., Nikolaevskii Yu. A., “Mnogoobraziya Grassmana i grassmanov obraz podmnogoobrazii”, UMN, 46:2 (1991), 41–83 | MR | Zbl