The Riemannian Space of Kähler Metrics

Chapter
Part of the Lecture Notes in Mathematics book series (LNM, volume 2038)

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.

Keywords

Symmetric Space Curvature Tensor Cohomology Class Riemannian Space Geodesic Equation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  1. 1.LATP, CNRS & Université de MarseilleMarseille Cedex 13France

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