On some non-canonical abelian almost 3-contact structures on Lie groups

ADRIÁN ANDRADA; GIULIA DILEO

Congreso; Mathematical Congress of the Americas; 2021

UBA

In a recent work with G. Dileo [AD], we introduced the notion of abelian almost 3-contact structure on Lie groups, and studied their algebraic and geometrical properties. Among these structures we highlighted a particular class, called canonical, which admit a compatible metric together with a metric connection with skew-symmetric torsion.The aim of this talk is to introduce a family of non-canonical abelian almost 3-contact structures, which are closely related to 2-step nilpotent Lie groups with left invariant hypercomplex structures. The Lie groups carrying these structures are not solvable nor semisimple, and we show that some of them admit co-compact discrete subgroups. We study geometrical properties of some compatible metrics.