Definition:Stiefel Manifold

Definition
Let $n \in \N_{> 0}$ be a natural number.

Let $k \in \N_{> 0}$ be a natural number such that $0 < k < n$.

The set $\map {V_k} {\R^n}$ of all orthonormal $k$-frames of $\R^n$ is called a Stiefel manifold.

That is, a Stiefel manifold is the set $\map {V_k} {\R^n}$ of orthonormal ordered $k$-tuples of vectors in $\R^n$.