arXiv 1105.21882011-05-11math.CVmath.DG

Geodesics in the space of Kähler metrics

László Lempert, Liz Vivas

发表信息：: Duke Math. J. 162, no. 7 (2013), 1369-1381
DOI：: 10.1215/00127094-2142865

英文摘要：

Let (X,ω) be a compact Kähler manifold. As discovered in the late 1980s by Mabuchi, the set H_0 of Kähler forms cohomologous to ωhas 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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