8 feb 2024 -- 15:30
Geometry in Como (hybrid)
Abstract.
Hyperkähler with torsion (HKT for short) manifolds are smooth manifolds endowed with a 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 hyperkähler 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.