Geodesic
Non-Parallelizability of Grassmann Manifolds
Canadian mathematical bulletin, Tome 27 (1984) no. 1, pp. 127-128

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The fact that no real Grassmann manifolds G k(Rn) are parallelizable (or even stably parallelizable) except for the obvious cases G1R2≅S1, G1(R4)≅G3(R4) ≅ RP3, and G1(R8)≅ G7(R8) ≅ RP7 was first noted by Hiller and Stong. Their work in turn depends on induction and the work of Oproiu, who examined detailed calculations of Stiefel-Whitney classes for k = 2, 3. In this note we give a short proof of this result, using elementary results from K-theory, that also covers the complex and quaternionic Grassmann manifolds.
DOI : 10.4153/CMB-1984-019-x
Mots-clés : 55N15, 57N25, 53C30 
Trew, S.; Zvengrowski, P. Non-Parallelizability of Grassmann Manifolds. Canadian mathematical bulletin, Tome 27 (1984) no. 1, pp. 127-128. doi: 10.4153/CMB-1984-019-x
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     year = {1984},
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     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1984-019-x/}
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