Locally conformally Symplectic structures on nilpotent Lie algebras and almost abelian Lie algebras

MARCOS ORIGLIA; ADRIÁN ANDRADA

Petrolinas

Congreso; V Latin American Conference on Lie Groups and Geometry; 2014

Universidade Federal do Vale do São Francisco

Locally conformally symplectic or LCS forms were introduced by Lee and Vaisman. They are non-degenerate 2-forms ω for which there exists a closed 1-form θ called the Lee form, satisfying dω = θ ∧ ω.In the first part of the talk we study LCS structures on nilpotent Lie algebras. We point out a connection between LCS structures and both contact pairs and contact geometry. We give a complete list of 6-dimensional nilpotent Lie algebras which admit LCS structures. In the second part we characterize the unimodular almost abelian Lie groups that admit left-invariant LCS structures and we study the existence of lattices in dimension 4.