Different geometries on the space of Kaehler and Sasakian metrics

speaker: David Petrecca (Leibniz Universität Hannover)

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.

timetable:
Fri 15 May, 15:10 - 16:00, Sala Conferenze Centro De Giorgi
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