# Different geometries on the space of Kaehler and Sasakian metrics

##
David Petrecca
(Leibniz Universität Hannover)

created by daniele on 28 Mar 2015

modified on 27 Apr 2015

15 may 2015
-- 15:10

Sala Conferenze, Collegio Puteano, Pisa

**Abstract.**

On a closed Kaehler manifold, the space of all Kaehler 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.