14 mar 2023 -- 14:30
Differential Geometry Seminar Torino (online)
Abstract.
Real and complex Monge-Ampere equations are classical and play a central role in several areas of analysis and geometry. More recently, quaternionic analogues of them were introduced and studied. In this talk we introduce what we call octonionic Kahler metrics on a class of 16-manifolds with an octonionic structure (e.g. on 16-tori). They are analogous to Kahler metrics on complex manifolds. We prove a version of the local ddc lemma for them. Then for such metrics we introduce an analogue of the Calabi problem. This is a Monge-Ampere equation in two octonionic variables. The problem is solved under extra assumptions on the manifolds (e.g. for 16-dimensional tori).
----------------------------------------------------------------------------------
If you would like to attend the talk remotely, please send an e-mail to dgseminar.torino@gmail.com