Abstract：

The existence and search of special metrics plays a remarkably important role in Differential Geometry. After a brief overview of basic definitions and facts in hypercomplex Geometry, we will discuss certain notions of special metrics in the hypercomplex setting, focusing on the consequences of their existence. We will also introduce an Einstein condition for hyperhermitian metrics and describe the similarities with the Kähler-Einstein case. The talk is based on a joint work with Elia Fusi.