Geometria Complessa e Geometria Differenziale
Geometria Complessa e Geometria Differenziale
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A Complex Geometry Day

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 L2, 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.

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