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

2016/11/30 by Adrián Andrada, A. Andrada, Marcos Origlia +1 · 2 citations
Mathematics · #Algebraic Geometry and Number Theory #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #math.DG #msc:22E25 #msc:22E40 #msc:53C15 #msc:53C55 #msc:53D05

paper · pdf · doi:10.1007/s00229-017-0938-3

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

arxiv created 2017/04/12 · crossref issued 2017/04/28 · crossref published 2017/04/28 · crossref published-online 2017/04/28 · openalex publication_date 2017/04/28 · crossref created 2017/04/28 · crossref deposited 2018/02/13 · crossref published-print 2018/03/01 · arxiv updated 2020/04/06 · openalex created_date 2025/10/10 · crossref indexed 2026/07/30 · openalex updated_date 2026/07/30

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.

Citations

• Curvatures of left invariant metrics on lie groups

Cited by

• A non-Vaisman LCK solvmanifold associated to a one-dimensional extension of a 2-step nilmanifold
• Integrable LCK manifolds

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