Geodesic
Classification of multidimensional submanifolds in Euclidean space with a~totally geodesic Gauss image
Sbornik. Mathematics, Tome 76 (1993) no. 1, pp. 225-246

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A complete classification is given of submanifolds that have a totally geodesic Gauss image in the ambient Grassmann manifold. The arguments are based on a study of the tangent space to the Gauss image of the submanifold and Cartan's theorem on totally geodesic submanifolds of symmetric spaces. 
@article{SM_1993_76_1_a12,
     author = {Yu. A. Nikolaevskii},
     title = {Classification of multidimensional submanifolds in {Euclidean} space with a~totally geodesic {Gauss} image},
     journal = {Sbornik. Mathematics},
     pages = {225--246},
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     volume = {76},
     number = {1},
     year = {1993},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1993_76_1_a12/}
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Yu. A. Nikolaevskii. Classification of multidimensional submanifolds in Euclidean space with a~totally geodesic Gauss image. Sbornik. Mathematics, Tome 76 (1993) no. 1, pp. 225-246. http://geodesic.mathdoc.fr/item/SM_1993_76_1_a12/