Geometry of unitary orbits of oblique projections

Abstract

We study those orbits of oblique projections under the action of the full unitary group of a Hilbert space H, which are submanifolds of B(H). We also consider orbits under the Schatten unitaries, and obtain a partial characterization of the submanifold condition for these orbits. Finsler metrics are introduced, and the minimality of metric geodesics is investigated.