# An overview on closed $G_2$-structures

##
Anna Fino
(Dipartimento di Matematica, Università di Torino)

created by bazzoni on 13 Apr 2022

modified on 18 May 2022

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.