Geodesic
On the Grassmanian image of submanifolds $F^n\subset E^{n+m}$ in which codimension does not exceed the dimension
Žurnal matematičeskoj fiziki, analiza, geometrii, Tome 5 (1998) no. 1, pp. 125-133 Cet article a éte moissonné depuis la source Math-Net.Ru

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A. A. Borisenko's hypothesis is studied: every tangent space of the Grassman image of a regular submanifold $F^n\subset E^{n+m}$ contains a two-dimensional plane $\pi$ such that the sectional curvature of the Grassman manifold $G_{n,n+m}$ in $\pi$ is less or equal to $1$. 
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     author = {V. M. Savel'ev},
     title = {On the {Grassmanian} image of submanifolds $F^n\subset E^{n+m}$ in which codimension does not exceed the dimension},
     journal = {\v{Z}urnal matemati\v{c}eskoj fiziki, analiza, geometrii},
     pages = {125--133},
     year = {1998},
     volume = {5},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/JMAG_1998_5_1_a9/}
}
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V. M. Savel'ev. On the Grassmanian image of submanifolds $F^n\subset E^{n+m}$ in which codimension does not exceed the dimension. Žurnal matematičeskoj fiziki, analiza, geometrii, Tome 5 (1998) no. 1, pp. 125-133. http://geodesic.mathdoc.fr/item/JMAG_1998_5_1_a9/