Complex structures on the Iwasawa manifold

2001/12/28 by Georgios Ketsetzis, Simon Salamon, Ketsetzis, Georgios +1
Mathematics · #22E25 (Secondary) #53C15 (Primary) 32G05 #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Homotopy and Cohomology in Algebraic Topology #math.DG #msc:22E25 #msc:32G05 #msc:53C15

paper · pdf · doi:10.48550/arxiv.math/0112295

arxiv created 2001/12/28 · openalex publication_date 2001/12/28 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

We identify the space of left-invariant oriented complex structures on the complex Heisenberg group, and prove that it has the homotopy type of the disjoint union of a point and a 2-sphere.

Citations

• Complex structures on nilpotent Lie algebras
• On the Cohomology of Compact Homogeneous Spaces of Nilpotent Lie Groups

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• Kähler submanifolds in Iwasawa manifolds
• Left-invariant almost complex structures on the higher dimensional Kodaira-Thurston manifolds
• Left invariant complex structures on U(2) and SU(2)xSU(2) revisited
• On cotangent manifolds, complex structures and generalized geometry