Abstract. We study those orbits of oblique projections under the action of the full unitary group of a Hilbert space ${\cal H}$, which are submanifolds of ${\cal B}({\cal H})$. 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.

AMS Subject Classification (1991): 22E65, 58E50, 58B20

Keyword(s): oblique projections, unitary orbits

Received June 23, 2009, and in revised form November 20, 2009. (Registered under 82/2009.)