Almost Hermitian Geometry on Six Dimensional Nilmanifolds

2000/07/11 by Elsa Abbena, E. Abbena, Sergio Garbiero +6 · 2 citations
Mathematics · #17B30 #51A05 #53C15 #53C55 #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Geometry and complex manifolds #math.DG #msc:17B30 #msc:51A05 #msc:53C15 #msc:53C55

paper · pdf · doi:10.48550/arxiv.math/0007066

22 pages, 2 figures

arxiv created 2000/07/11 · openalex publication_date 2000/07/11 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The fundamental 2-form of an invariant almost Hermitian structure on a 6-dimensional Lie group is described in terms of an action by SO(4)xU(1) on complex projective 3-space. This leads to a combinatorial description of the classes of almost Hermitian structures on the Iwasawa and other nilmanifolds.

Citations

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

Cited by

• The exterior derivative of the Lee form of almost Hermitian manifolds
• The moduli space of left-invariant metrics of a class of six-dimensional nilpotent Lie groups

Related

• Hermitian structures on six-dimensional almost nilpotent solvmanifolds
• Left-invariant almost para-complex structures on six-dimensional nilpotent Lie groups
• Hermitian structures on six dimensional nilmanifolds
• Balanced Hermitian geometry on 6-dimensional nilmanifolds
• Hermitian structures on a class of almost nilpotent solvmanifolds