Geometria Complessa e Geometria Differenziale
Geometria Complessa e Geometria Differenziale
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Cohomological properties of hypercomplex manifolds

Nicoletta Tardini (Università di Parma)

created by daniele on 16 Feb 2023
modified on 15 Apr 2023

31 may 2023 -- 11:30

Aula Tricerri, DIMaI, Firenze

Seminari di Geometria del Dini

Abstract.

Hyperk\"ahler with torsion (HKT for short) manifolds are smooth manifolds endowed with an hypercomplex structure $(I,J,K)$ and a real and positive (in the quaternionic sense) $\partial$-closed $(2,0)$ form (here the bidegree and $\partial$ are taken with respect to the complex structure $I$). Examples of these manifolds are hyperk\"ahler manifolds. We will discuss the cohomological behavior of HKT manifolds and we will present some numerical characterizations for the existence of such metrics. These are joint works with Giovanni Gentili and Mehdi Lejmi.

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