On normal sections of Stiefel submanifold (Q2770037)

The Stiefel manifold \(V_{n,k}\), consisting of \(k\)-frames (systems of \(k\) orthonormal vectors) in Euclidean \(\mathbb{R}^n\), is realized as a submanifold of dimension \(nk-\frac 12 k(k+1)\) in \(\mathbb{R}^{nk}\). Such a \(V_{n,k}\) is considered as the first standard imbedding of the real projective space. It is shown that this imbedding has parallel second fundamental form and thus, due to a result by \textit{K. Arslan} and \textit{A. West} [Bull. Lond. Math. Soc. 28, 88-92 (1996; Zbl 0847.53011)], has pointwise 2-planar normal sections.