Hilbert-Schmidt groups as infinite-dimensional Lie groups and their Riemannian geometry

Research paper by Maria Gordina

Indexed on: 14 Jun '05Published on: 14 Jun '05Published in: Mathematics - Differential Geometry


We describe the exponential map from an infinite-dimensional Lie algebra to an infinite-dimensional group of operators on a Hilbert space. Notions of differential geometry are introduced for these groups. In particular, the Ricci curvature, which is understood as the limit of the Ricci curvature of finite-dimensional groups, is calculated. We show that for some of these groups the Ricci curvature is $-\infty$.