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.