Geodesic
Geometry of real Grassmannian manifolds. VI
Zapiski Nauchnykh Seminarov POMI, Geometry and topology. Part 3, Tome 252 (1998), pp. 121-133 
S. E. Kozlov. Geometry of real Grassmannian manifolds. VI. Zapiski Nauchnykh Seminarov POMI, Geometry and topology. Part 3, Tome 252 (1998), pp. 121-133. http://geodesic.mathdoc.fr/item/ZNSL_1998_252_a10/
@article{ZNSL_1998_252_a10,
     author = {S. E. Kozlov},
     title = {Geometry of real {Grassmannian} {manifolds.~VI}},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {121--133},
     year = {1998},
     volume = {252},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1998_252_a10/}
}
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Using invariants of the canonical decomposition of the tangent vector of an arbitrary geodesic in the real Grassmannian variety $G_{p,n}^+$, we give a complete description of the set of conjugate points. For an arbitrary shortest curve, a nontrivial variation with fixed endpoints is constructed. The separation sets for the Grassmannian $G_{2,4}^+$ and its tangent bundle are found.