Geodesics in the space of K\"ahler metrics
Complex Variables
2019-12-19 v1 Differential Geometry
Abstract
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".
Keywords
Cite
@article{arxiv.1105.2188,
title = {Geodesics in the space of K\"ahler metrics},
author = {László Lempert and Liz Vivas},
journal= {arXiv preprint arXiv:1105.2188},
year = {2019}
}