# Different geometries on the space of Kähler and Sasakian metrics

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David Petrecca
(Leibniz Universität Hannover)

created by daniele on 13 Apr 2015

modified on 20 May 2015

3 jul 2015
-- 10:00

Bielefeld University

**Abstract.**

On a closed Kähler manifold, the space of all Kähler metrics in a fixed cohomology class has a natural structure of infinite dimensional manifold. On it, several (weak) Riemannian metrics can be assigned and the most studied ones are called $L^2$, Calabi and Gradient (or Dirichlet) metric. I will recall known results about their different geometries and write down and compare the relative geodesic equations as PDEs on the manifold. Finally I will discuss my contribution, joint with S. Calamai and K. Zheng, about the geodesic equation of the gradient metric and of the Ebin metric restricted to the (similarly defined) space of Sasakian metrics.