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arXiv · 1205.0840

Weak geodesics in the space of Kähler metrics

Tamás Darvas·László Lempert
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Abstract

Given a compact Kähler manifold (X,ω_0), according to Mabuchi, the set of Kähler forms cohomologous to ω_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.

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Tamás Darvas, László Lempert. 2012-05-04. Weak geodesics in the space of Kähler metrics. https://arxiv.org/abs/1205.0840

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