Conformal Minimal Foliations on Semi-Riemannian Lie Groups

2020/12/15 by Elsa Ghandour, Ghandour, Elsa, Sigmundur Gudmundsson +3
Mathematics · Biochemistry, Genetics and Molecular Biology · #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Dermatological and Skeletal Disorders

paper · pdf · doi:10.48550/arxiv.2012.08627

Abstract

We study left-invariant foliations \mathcal F on semi-Riemannian Lie groups G generated by a subgroup K. We are interested in such foliations which are conformal and with minimal leaves of codimension two. We classify such foliations \mathcal F when the subgroup K is one of the important SU(2), SL₂(\mathbb R), SU(2)\timesSU(2), SU(2)\timesSL₂(\mathbb R), SU(2)\timesSO(2), SL₂(\mathbb R)\timesSU(2). This way we construct new multi-dimensional families of Lie groups G carrying such foliations in each case. These foliations \mathcal F produce local complex-valued harmonic morphisms on the corresponding Lie group G.

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