\begin{definition}[Definition:Grassmann Manifold]
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 $\map {G_k} {\R^n}$ of $k$-dimensional linear subspaces of $\R^n$ is called a '''Grassmann manifold'''.
\end{definition}