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15 May 2013 Geodesics in the space of Kähler metrics
László Lempert, Liz Vivas
Duke Math. J. 162(7): 1369-1381 (15 May 2013). DOI: 10.1215/00127094-2142865

Abstract

Let (X,ω) be a compact Kähler manifold. As discovered in the late 1980s by Mabuchi, the set H0 of Kähler forms cohomologous to ω has the natural structure of an infinite-dimensional Riemannian manifold. We address the question of whether any two points in H0 can be connected by a smooth geodesic and show that the answer, in general, is “no.”

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László Lempert. Liz Vivas. "Geodesics in the space of Kähler metrics." Duke Math. J. 162 (7) 1369 - 1381, 15 May 2013. https://doi.org/10.1215/00127094-2142865

Information

Published: 15 May 2013
First available in Project Euclid: 10 May 2013

zbMATH: 1275.32020
MathSciNet: MR3079251
Digital Object Identifier: 10.1215/00127094-2142865

Subjects:
Primary: 32Q15
Secondary: 32W20

Rights: Copyright © 2013 Duke University Press

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Vol.162 • No. 7 • 15 May 2013
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