Invariant $G_2$-structures with free-divergence torsion tensor

Início: 22/04/2022 17:00

Término: 22/04/2022 18:00

Palestrante: Andrés Moreno (Unicamp)

E-mail do Palestrante: amoreno@unicamp.br

Resumo: A $G_2$-structure with free divergence torsion can be interpreted as a critical point of the energy functional, restricted to its isometric class. Hence, it represents the better $G_2$-structure in a given family. These kinds of $G_2$-structures are an alternative for the study of $G_2$-geometry, in cases when the torsion free problem is either trivial or obstructed. In general, there are some known classes of $G_2$-structures with free-divergence torsion, namely closed and nearly parallel $G_2$-structures. In this talk, we are going to present some unknown classes of invariant $G_2$-structures with free divergence torsion, specifically in the context of the 7-sphere and of the solvable Lie groups with a codimension-one Abelian normal subgroup.