Geodesic
Geometry of real Grassmanian manifolds.~V
Zapiski Nauchnykh Seminarov POMI, Geometry and topology. Part 3, Tome 252 (1998), pp. 104-120

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The curvature transform is calculated for the Grassmanian manifold $G^+_{2,4}$ with the help of the Riemannian decomposition $G^+_{2,4}\cong S^2\times S^2$. Together with the author's earlier results about almost geodesic submanifolds of $G^+_{p,n}$, this makes it possible to give the formula for the Riemannian curvature in $G^+_{p,n}$. This formula allows us to give a geometrical description of two-dimensional directions with maximal sectional curvature in $G^+_{p,n}$. 
@article{ZNSL_1998_252_a9,
     author = {S. E. Kozlov},
     title = {Geometry of real {Grassmanian} {manifolds.~V}},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {104--120},
     publisher = {mathdoc},
     volume = {252},
     year = {1998},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1998_252_a9/}
}
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S. E. Kozlov. Geometry of real Grassmanian manifolds.~V. Zapiski Nauchnykh Seminarov POMI, Geometry and topology. Part 3, Tome 252 (1998), pp. 104-120. http://geodesic.mathdoc.fr/item/ZNSL_1998_252_a9/