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The purpose of this note is to prove the result stated in the title by constructing a Gauss map for the standard embedding      V k ( R n ) ⊂  R n k {V_k}({{\mathbf {R}}^n}) \subset {{\mathbf {R}}^{nk}}      .

The parallelizability of the Stiefel manifolds 𝑉_{𝑘}(𝑅ⁿ): 𝑘≥3