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 $\R^n$.

Source of Name

This entry was named for Eduard Ludwig Stiefel.

Sources

• 2018: John M. Lee: Introduction to Riemannian Manifolds (2nd ed.) ... (previous) ... (next): $\S 2$: Riemannian Metrics. Problems