Tamás Darvas
Published 2019-02-16Version 1
Given a compact K\"ahler manifold, we prove that all global isometries of the space of K\"ahler metrics are induced by biholomorphisms and anti-biholomorphisms of the manifold. In particular, there exist no global symmetries for Mabuchi's metric. Moreover, we show that the Mabuchi completion does not even admit local symmetries. Closely related to these findings, we provide a large class of metric geodesic segments that can not be extended at one end, pointing out the first such examples in the literature.
Geometry and Topology of the space of Kähler metrics on singular varieties
Long geodesics in the space of Kähler metrics
On the $C^{1,1}$ regularity of geodesics in the space of Kähler metrics
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