Geodesic
Canonical representation of tangent vectors of Grassmannians
Zapiski Nauchnykh Seminarov POMI, Geometry and topology. Part 9, Tome 329 (2005), pp. 147-158 Cet article a éte moissonné depuis la source Math-Net.Ru

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The structure of the tangent bundle of the real Grassmann manifold $G^+_{p,n}$ under the Plücker embedding (in the exterior algebra of the initial Euclidean space) is studied. Explicit expressions for the relation between decompositions of a tangent vector with respect to different bases of the tangent space are obtained, and a constructive method yielding the canonical (= simplest) decomposition is presented. 
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     author = {M. Yu. Nikanorova},
     title = {Canonical representation of tangent vectors of {Grassmannians}},
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M. Yu. Nikanorova. Canonical representation of tangent vectors of Grassmannians. Zapiski Nauchnykh Seminarov POMI, Geometry and topology. Part 9, Tome 329 (2005), pp. 147-158. http://geodesic.mathdoc.fr/item/ZNSL_2005_329_a11/

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