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arXiv · 1105.2188

Geodesics in the space of K\"ahler metrics

László Lempert·Liz Vivas
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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".

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László Lempert, Liz Vivas. 2011-05-11. Geodesics in the space of K\"ahler metrics. https://doi.org/10.1215/00127094-2142865

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