%0 Journal Article
%T Geodesics in the space of K£¿hler metrics
%A L¨¢szl¨® Lempert
%A Liz Vivas
%J Mathematics
%D 2011
%I arXiv
%X Let (X,\omega) be a compact K\"ahler manifold. As discovered in the late 1980s by Mabuchi, the set H_0 of K\"ahler forms cohomologous to \omega has the natural structure of an infinite dimensional Riemannian manifold. We address the question whether any two points in H_0 can be connected by a smooth geodesic, and show that the answer, in general, is "no".
%U http://arxiv.org/abs/1105.2188v1