On the linearly independent vector fields on Grassmann manifolds

In this paper are found θ(n)θ(n) linearly independent vector fields on the Grassmann manifold Gk(V)Gk(V) of k-planes in n-dimensional Euclidean vector space if k   is odd number, where θ(n)θ(n) is the maximal number of linearly independent vector fields on Sn−1Sn−1, i.e. skewsymmetric anticommuting complex structures on RnRn.