Lattices in almost abelian Lie groups with locally conformal Kähler or symplectic structures

Abstract

We study the existence of lattices in almost abelian Lie groups that admit left invariant locally conformal Kähler or locally conformal symplectic structures in order to obtain compact solvmanifolds equipped with these geometric structures. In the former case, we show that such lattices exist only in dimension $4$, while in the latter case we provide examples of such Lie groups admitting lattices in any even dimension.

Minor modifications added to the first version, the statement of Theorem 3.3 was improved. To appear in Manuscripta matematica

References in corpus (4)

• Supersymmetry breaking branes on solvmanifolds and de Sitter vacua in string theory
• Compact homogeneous lcK manifolds are Vaisman
• Lattices, cohomology and models of six dimensional almost abelian solvmanifolds
• Locally conformally Kähler structures on unimodular Lie groups

Cited by in corpus (13)

• Locally conformally Kähler structures on four-dimensional solvable Lie algebras
• Hypercomplex almost abelian solvmanifolds
• The structure of almost Abelian Lie algebras
• Applications of the quaternionic Jordan form to hypercomplex geometry
• Almost Abelian Lie groups, subgroups and quotients
• Locally conformally product structures on solvmanifolds
• On certain class of locally conformal symplectic structures of the second kind
• Complex Symplectic Lie Algebras with Large Abelian Subalgebras
• Harmonic $G_2$-structures on almost Abelian Lie groups
• Locally conformal symplectic structures on Lie algebras of type I and their solvmanifolds
• Integrable LCK manifolds
• On Weyl-reducible conformal manifolds and lcK structures
• The hard Lefschetz duality for locally conformally almost Kähler manifolds