26 février 2020

Nicoletta Tardini (Université de Turin)
Special Hermitian metrics on complex manifolds

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Lieu : Salle 3L8

Résumé : A very special class of complex manifolds is realized by Kähler manifolds, namely complex manifolds admitting a Hermitian metric whose fundamental form is symplectic. The existence of such a metric implies sev- eral cohomological obstructions as the validity of the ∂∂-lemma. We will discuss the relations between this property and the Bott-Chern cohomol- ogy on complex non-Kähler manifolds. Moreover, several generalizations of Kähler metrics have been introduced by imposing that the fundamental form of a Hermitian metric (or its powers) is in the kernel of a suitable differential operator. One could expect that these metrics arise as critical points of naturally defined functionals on the space of Hermitian metrics. We will investigate some of these functionals, restricted to a conformal class of normalized Hermitian metrics, discussing the geometric meaning of their critical points. These are joint works with Daniele Angella, Nicolina Istrati and Alexandra Otiman.

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