Locally conformal Kahler or symplectic structures on compact solvmanifolds

MARCOS ORIGLIA

Hanover

Conferencia; Lie group actions in Riemannian Geometry; 2017

Dartmouth College

We consider locally conformal Kahler (LCK) manifolds, that is, a Hermitianmanifold (M; J; g) such that on each point there exists a neighborhood wherethe metric is conformal to a Kahler metric. Equivalently, (M; J; g) is LCK ifand only if there exists a closed 1-form such that d! = ^ !, where ! is thefundamental 2-form determined by the Hermitian structure. The 1-form iscalled the Lee form. On the other hand, the concept of LCK structure can begeneralized to the notion of locally conformal symplectic (LCS) structure, thatis a pair (!; ) satisfying d! = ^ !, where ! is a non-degenerate 2-form and is a closed 1-form.In this work we study left invariant LCK or LCS structures on solvable Liegroups and the existence of lattices (co-compact discrete subgroups) on theseLie groups in order to obtain compact solvmanifolds equipped with these kindof locally conformal geometric structures.