Surjective isometries on Grassmann spaces

Let HH be a complex Hilbert space, n   a given positive integer and let Pn(H)Pn(H) be the set of all projections on HH with rank n  . Under the condition dimH⩾4n, we describe the surjective isometries of Pn(H)Pn(H) with respect to the gap metric (the metric induced by the operator norm).