LCK or LCS structures on almost abelian Lie groups

MARCOS ORIGLIA

Simposio; Heidelberg Laureate Forum; 2017

We consider locally conformal K¨ ahler (LCK) manifolds, that is, a Hermitian manifold (M;J;g) such that on each point there exists a neighborhood where the metric is conformalto a K¨ ahler metric. On the other hand, the concept of LCK structure can be generalized to the notion of locally conformal symplectic (LCS) structure, that is, a smooth manifoldM equipped with a non-degenerate 2 form w such that on each point there exists a neighborhood where w is conformal to a symplectic form.In this work we study left invariant LCK or LCS structures on almost abelian Lie groups and the existence of lattices (co-compact discrete subgroups) on these Lie groups inorder to obtain compact solvmanifolds equipped with these kind of locally conformal geometric structures.