Embeddings of Stiefel manifolds and related homogeneous spaces into Euclidean space (Q1076378)

The aim of this note is the construction of embeddings of Stiefel manifolds (both real, complex and quaternionic) into Euclidean spaces of ''low'' codimension. In most cases, the normal bundle of the embedding is shown to split off ''big'' trivial bundles, which is useful for inductive constructions. Part of the paper is an adaptation to homogeneous spaces of methods using representations developed by \textit{G. Walker} and \textit{R. M. Wood} [Proc. Edinb. Math. Soc., II. Ser. 27, 25-29 (1984; Zbl 0532.57018)].