Non Kaehler solvmanifolds with generalized Kaehler structure

2007/02/06 by Anna Fino, Fino, Anna, Адриано Томассини +2
Mathematics · #22E25 #53C15 #53C56 #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Geometry and complex manifolds #math.DG #msc:22E25 #msc:53C15 #msc:53C56

paper · pdf · doi:10.48550/arxiv.math/0702164

New title. To appear in J. Sympl. Geom

openalex publication_date 2007/02/06 · arxiv created 2008/07/09 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We construct a compact 6-dimensional solvmanifold endowed with a non-trivial invariant generalized Kähler structure and which does not admit any Kähler metric. This is in contrast with the case of nilmanifolds which cannot admit any invariant generalized Kähler structure unless they are tori.

Citations

• Curvatures of left invariant metrics on lie groups

Related

• Kähler Solvmanifolds
• Hermitian structures on six-dimensional almost nilpotent solvmanifolds
• SKT and Tamed Symplectic structures on solvmanifolds
• Special non-Kähler metrics -- old and new
• Hermitian structures on six dimensional nilmanifolds