Grassmann Manifold

A special case of a Flag Manifold. A Grassmann manifold is a certain collection of vector Subspaces of a Vector Space. In particular, $G_{n,k}$ is the Grassmann manifold of $k$-dimensional subspaces of the Vector Space $\Bbb{R}^n$. It has a natural Manifold structure as an orbit-space of the Stiefel Manifold $V_{n,k}$ of orthonormal $k$-frames in $\Bbb{R}^n$. One of the main things about Grassmann manifolds is that they are classifying spaces for Vector Bundles.