In 1958, I. M. James raised two fundamental questions about octonionic Stiefel spaces \(V_{k}(\mathbb{O}^{n})\) . The first breakthrough was made by Qian, Tang, Yan in 2022. The present paper is divided into two parts. The first one shows that neither of two natural projections \(V_{k+2}(\mathbb{O}^n) \xrightarrow{\pi_2} V_k(\mathbb{O}^n)\) and \(V_{k+3}(\mathbb{O}^n) \xrightarrow{\pi_3} V_k(\mathbb{O}^n)\) is a fiber bundle. The second one proves the parallelizability of closed manifold Ωl,m, which contains \(V_{3}(\mathbb{O}^n)\) as a special case.
