Grassmannian manifolds are extremely important in (differential) geometry. Thus, we want to add them to the catalog of manifolds in Sage.

The following notes introduce charts and their transition maps very straightforwardly:

http://www.math.toronto.edu/mgualt/courses/18-367/docs/DiffGeomNotes-2.pdf

However, the number of charts grows extremely fast, namely ncr(n,k). One approach could be to parallelize the initialization process to reach at least low dimensional Grassmannians in a reasonable time.

Apart from that, it could be enough to start with only one chart since this should already cover enough (in particular, everything except a set of measure zero). That should give enough freedom to do almost everything on Grassmannians already.

Part of metaticket #30189.

CC: @egourgoulhon @tscrim @tobiasdiez

Component: manifolds

Issue created by migration from https://trac.sagemath.org/ticket/31249