Geodesic
Totally umbilical submanifolds in $G(2,n)$. III
Žurnal matematičeskoj fiziki, analiza, geometrii, Tome 3 (1996) no. 3, pp. 339-355
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This paper is the continuation of the papers with the same title, I, II, published in Ukr. geom. sb. (1992, 1993), iss. 34, 35. Complete classification of totally umbilical surfaces in the Grassmann manifold $G(2,n)$ is presented. 
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Yu. A. Nikolaevskii. Totally umbilical submanifolds in $G(2,n)$. III. Žurnal matematičeskoj fiziki, analiza, geometrii, Tome 3 (1996) no. 3, pp. 339-355. http://geodesic.mathdoc.fr/item/JMAG_1996_3_3_a8/