A Grassmann manifold is a special case of a flag manifold. A Grassmann manifold is a certain collection of vector subspaces
of a vector space. In particular, 
is the Grassmann manifold of 
-dimensional subspaces of the vector
space 
. It has a natural manifold
structure as an orbit-space of the Stiefel manifold 
of orthonormal 
-frames in 
. One of the main things about
Grassmann manifolds is that they are classifying spaces for vector
bundles.
Grassmann Manifold
See also
Grand Tour, GrassmannianExplore with Wolfram|Alpha
Cite this as:
Weisstein, Eric W. "Grassmann Manifold." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/GrassmannManifold.html