This item is available under a Creative Commons License for non-commercial use only
Pure mathematics, Applied mathematics, Atomic, Molecular and Chemical Physics
We establish geometric properties of Stiefel and Grassmann manifolds which arise in relation to Slatertype variational spaces in many-particle Hartree-Fock theory and beyond. In particular, we prove thatthey are analytic homogeneous spaces and submanifolds of the space of bounded operators on the single-particle Hilbert space. As a by-product we obtain that they are complete Finsler manifolds. These geometric properties underpin state-of-the-art results on existence of solutions to Hartree-Fock type equations.
Journal of Geometry and Physics (2012), to appear. Online: http://www.sciencedirect.com/science/article/pii/S0393044012000927