Geodesic
Isometric equivalence of directions in Riemannian symmetric spaces
Zapiski Nauchnykh Seminarov POMI, Geometry and topology. Part 9, Tome 329 (2005), pp. 56-57 Cet article a éte moissonné depuis la source Math-Net.Ru

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It is proved that there exists an isometry of the real Graccmann manifold that puts into coincidence two one-dimensional tangent directions of a totally geodesic 2-surface with nonzero Gauss curvature. 
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     author = {S. E. Kozlov},
     title = {Isometric equivalence of directions in {Riemannian} symmetric spaces},
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     url = {http://geodesic.mathdoc.fr/item/ZNSL_2005_329_a3/}
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S. E. Kozlov. Isometric equivalence of directions in Riemannian symmetric spaces. Zapiski Nauchnykh Seminarov POMI, Geometry and topology. Part 9, Tome 329 (2005), pp. 56-57. http://geodesic.mathdoc.fr/item/ZNSL_2005_329_a3/

[1] S. E. Kozlov, “Geometriya veschestvennykh grassmanovykh mnogoobrazii”, Zap. nauchn. semin. POMI, 246 (1997), 84–107 | MR | Zbl