Curvature of the Slater determinant manifold

Abstract

The mapping of a straight line in the particle-hole space onto the manifold of Slater determinants is found to induce a trajectory whose curvature is between 1 and 3. This curvature depends on the direction of the line, which renders the particle-hole space anisotropic. There are indications that collective motion induces a large curvature of the path