Abelian almost contact structures and connections with skew-symmetric torsion

Início: 22/05/2020 17:00

Término: 22/05/2020 18:00

Palestrante: Adrian Andrada (Universidad Nacional de Córdoba)

E-mail do Palestrante:

Resumo: Abelian complex structures on Lie groups have proved to be very useful in several areas of differential and complex geometry. In particular, an abelian hypercomplex structure on a Lie group G (that is, a pair of anticommuting abelian complex structures), together with a compatible inner product, gives rise to an invariant hyperKähler with torsion (HKT) structure on G. This means that G admits a (unique) metric connection with skew-symmetric torsion (called the Bismut connection) which parallelizes the hypercomplex structure. In this talk we move to the odd-dimensional case and we introduce the notion of abelian almost contact structures on Lie groups. We study their properties and their relations with compatible metrics. Next we consider almost 3-contact Lie groups where each almost contact structure is abelian. We study their main properties and we give their classification in dimension 7. After adding compatible Riemannian metrics, we study the existence of a certain type of metric connections with skew symmetric torsion, introduced recently by Agricola and Dileo and called canonical connections. We provide examples of such groups in each dimension 4n+3 and show that they admit co-compact discrete subgroups, which give rise to compact almost 3-contact metric manifolds equipped with canonical connections.

Comentários: To participate in the webinar, please request the link to geodif@unicamp.br with subject "Webinar AmSur".