The Riemannian Space of Kähler Metrics
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.
KeywordsSymmetric Space Curvature Tensor Cohomology Class Riemannian Space Geodesic Equation
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