Locally conformally symplectic structures on nilpotent or almost abelian Lie groups

MARCOS ORIGLIA; ADRIÁN ANDRADA

Bedlewo

Conferencia; Workshop on Almost hermitian and contact geometry; 2015

Locally conformally symplectic (or LCS) forms were introduced by Lee andVaisman. They are non-degenerate 2-forms ω for which there exists a closed1-form θ, called the Lee form, satisfying dω = θ ∧ ω.In the first part of the talk we study left-invariant LCS structures on nilpo-tent Lie groups. We point out a connection between LCS structures and bothcontact pairs and contact geometry. We give a complete list of 6-dimensionalnilpotent Lie algebras which admit LCS structures. In the second part we char-acterize the unimodular almost abelian Lie groups that admit left-invariant LCSstructures and we study the existence of lattices in order to obtain examples ofcompact solvmanifolds with an LCS structure. Among these LCS structures,we determine which ones arise from a locally conformally Kähler metric.