Natural Almost Hermitian Structures on Conformally Foliated 4-Dimensional Lie Groups with Minimal Leaves

2022/03/03 by Emma Andersdotter Svensson, Svensson, Emma Andersdotter
Mathematics · #Algebraic Geometry and Number Theory #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.2203.01887

openalex publication_date 2022/03/03 · openalex created_date 2024/04/10 · openalex updated_date 2026/07/28

Abstract

Let (G,g) be a 4-dimensional Riemannian Lie group with a 2-dimensional left-invariant, conformal foliation F with minimal leaves. Let J be an almost Hermitian structure on G adapted to the foliation F. The corresponding Lie algebra \mathfrakg must then belong to one of 20 families \mathfrakg₁,…,\mathfrakg₂₀ according to S. Gudmundsson and M. Svensson. We classify such structures J which are almost Kähler (AK), integrable (I) or Kähler (K). Hereby, we construct 16 multi-dimensional almost Kähler families, 18 integrable families and 11 Kähler families.

Related

• Natural almost Hermitian structures on conformally foliated 4-dimensional Lie groups with minimal leaves
• Eight-Dimensional Hermitian Lie Groups Conformally Foliated by Minimal SU(2) × SU(2) Leaves
• Conformal Minimal Foliations on Semi-Riemannian Lie Groups
• Almost Hermitian Geometry on Six Dimensional Nilmanifolds
• Holomorphic harmonic morphisms from four-dimensional non-Einstein manifolds