Document Type
Article
Rights
This item is available under a Creative Commons License for non-commercial use only
Abstract
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.
DOI
http://doi.org10.21427/6hde-rn66
Recommended Citation
Journal of Geometry and Physics (2012), to appear. Online: http://www.sciencedirect.com/science/article/pii/S0393044012000927 doi:10.21427/6hde-rn66
Funder
Science Foundation Ireland
Included in
Analysis Commons, Atomic, Molecular and Optical Physics Commons, Materials Chemistry Commons, Partial Differential Equations Commons
Publication Details
To appear in Journal of Geometry and Physics (2012).
Online: http://www.sciencedirect.com/science/article/pii/S0393044012000927