Abstract
The goal of this lecture is to describe the Riemannian structure on the space of Kähler metrics (in a fixed cohomology class) on a compact complex manifold which was proposed by Mabuchi [Mab87] and further stud- ied by Semmes [Sem92], Donaldson [Don99], Chen and Calabi [Che00,CC02]. The lecture starts by explaining some of the difficulties encountered in this infinite dimensional setting.
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© 2012 Springer-Verlag Berlin Heidelberg
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Kolev, B. (2012). The Riemannian Space of Kähler Metrics. In: Guedj, V. (eds) Complex Monge–Ampère Equations and Geodesics in the Space of Kähler Metrics. Lecture Notes in Mathematics(), vol 2038. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-23669-3_6
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DOI: https://doi.org/10.1007/978-3-642-23669-3_6
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Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-23668-6
Online ISBN: 978-3-642-23669-3
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