Weak geodesics in the space of K\"ahler metrics
Complex Variables
2013-08-07 v1 Differential Geometry
Abstract
Given a compact K\"ahler manifold (X,\omega_0), according to Mabuchi, the set of K\"ahler forms cohomologous to \omega_0 has the natural structure of an infinite dimensional Riemannian manifold. We address the question whether points in this space can be joined by a geodesic, and strengthening previous findings of the second author with Vivas, we show that this cannot always be done even with a certain type of generalized geodesics.
Cite
@article{arxiv.1205.0840,
title = {Weak geodesics in the space of K\"ahler metrics},
author = {Tamás Darvas and László Lempert},
journal= {arXiv preprint arXiv:1205.0840},
year = {2013}
}