Projections with fixed difference: a Hopf-Rinow theorem

Esteban Andruchow, Gustavo Corach, Lázaro Recht

The set $D_{A_0}$, of pairs of orthogonal projections $(P,Q)$ in generic position with fixed difference $P-Q=A_0$, is shown to be a homogeneus smooth manifold: it is the quotient o…