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Session S23 - Group actions in Differential Geometry

Friday, July 16, 16:00 ~ 16:30 UTC-3

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

Adrián Andrada

Universidad Nacional de Córdoba - CONICET, Argentina   -   This email address is being protected from spambots. You need JavaScript enabled to view it.

In a recent work with G. Dileo [AD], we introduced the notion of \textit{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.

[AD] A. Andrada, G. Dileo, Odd dimensional counterparts of abelian complex and hypercomplex structures, to appear in \textit{Math. Nachr.}

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