Natural almost Hermitian structures on conformally foliated 4-dimensional Lie groups with minimal leaves

2022/01/11 by Emma Andersdotter Svensson, Svensson, Emma Andersdotter, Gudmundsson, Sigmundur
Mathematics · #53C43 #58E20 #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Differential Geometry (math.DG) #FOS: Mathematics #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.2201.03854

openalex publication_date 2022/01/11 · openalex created_date 2022/04/03 · 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. We classify such structures J which are almost K"ahler (\A\K), integrable (\I) or K"ahler (\K). Hereby we construct several new multi-dimensional examples in each class.

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