MERCOLEDI' 18 APRILE 2012
16:00-17:00, Sala Riunioni (Dip. Matematica)
SEMINARI DI GEOMETRIA'The Calabi metric for the space of Kaehler metrics'
Simone Calamai (Scuola Normale Superiore)
We follow an idea by Calabi (1953) to propose a Riemannian structure,
which we name after him, for the space of Kaehler metrics on a given
closed Kaehler manifold of any complex dimension. Building on the
Calabi conjecture we are able to prove that the Calabi metric admits a
rich geometry and its geodesics have explicit analytic expression.
Moreover the Calabi metric admits an isometric immersion in a portion
of an infinite sphere. We will discuss there features making
comparisons with the classical Mabuchi-Semmes-Donaldson metric.