Seminar “Analysis, geometry and topology”
Tuesday, July 22-nd, 13:00 o’clock, room 403 of IMI-BAS.
Elia Fusi, University of Torino.
Special metrics in hypercomplex geometry
Abstract: The existence of special hyperHermitian metrics plays an important role in the study of hypercomplex manifolds. In this talk, after a brief overview of the basic definitions in hypercomplex Geometry, we will discuss two of the main types of special metrics in the hypercomplex setting: quaternionic Gauduchon and strong HKT metrics. First of all, we will discuss sufficient and equivalent conditions for a quaternionic Gauduchon metric to exist. Afterwards, we will show that strong HKT and balanced hyperHermitian metrics cannot coexist on a compact non-hyperKähler manifold, proving a particular instance of the Fino-Vezzoni conjecture. Finally, we will introduce an Einstein condition for hyperHermitian metrics and describe the similarities with the Kähler-Einstein case.
This is a joint work with Giovanni Gentili.