19 may 2022 -- 17:00
Geometry in Como (online)
Abstract.
$G_2$-structures on 7-manifolds are defined by a closed positive 3-forms and constitute the starting point in various known and potential methods to obtain holonomy $G_2$-metrics. Although linear, the closed condition for a $G_2$-structure is very restrictive, and no general results on the existence of closed G2-structures on compact 7-manifolds are known. In the seminar I will review known examples of compact 7-manifolds admitting a closed $G_2$-structure. Moreover, I will discuss some results on exact $G_2$-structures and the behaviour of the Laplacian $G_2$-flow starting from a closed $G_2$-structure whose induced metric satisfies suitable extra conditions.