The manifold of finite rank projections in the space L(H)

Given a complex Hilbert space H and the von Neumann algebra L(H) of all bounded linear operators in H, we study the Grassmann manifold M of all projections in L(H) that have a fixed finite rank r. To do it we take the Jordan-Banach triple (or JB*-triple) approach which allows us to define a natural Levi-Civita connection on M by using algebraic tools. We identify the geodesics and the Riemann distance and establish some properties of M.
José M. Isidro < jmisidro@zmat.usc.es >