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2022 Conformal Minimal Foliations on Semi-Riemannian Lie Groups
Elsa Ghandour, Sigmundur Gudmundsson, Victor Ottosson
J. Geom. Symmetry Phys. 63: 1-20 (2022). DOI: 10.7546/jgsp-63-2022-1-20

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 groups $\mathrm{SU}(2)$, $\mathrm{SL}_2(\mathbb{R})$, $\mathrm{SU}(2)\times\mathrm{SU}(2)$, $\mathrm{SU}(2)\times\mathrm{SL}_2(\mathbb{R})$, $\mathrm{SU}(2)\times\mathrm{SO}(2)$, $\mathrm{SL}_2(\mathbb{R})\times\mathrm{SO}(2)$. 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 $G$. This means that they provide the existence of solutions to a difficult over-determined non-linear system of partial differential equations.

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Elsa Ghandour. Sigmundur Gudmundsson. Victor Ottosson. "Conformal Minimal Foliations on Semi-Riemannian Lie Groups." J. Geom. Symmetry Phys. 63 1 - 20, 2022. https://doi.org/10.7546/jgsp-63-2022-1-20

Information

Published: 2022
First available in Project Euclid: 29 April 2022

Digital Object Identifier: 10.7546/jgsp-63-2022-1-20

Rights: Copyright © 2022 Bulgarian Academy of Sciences, Institute of Mechanics

JOURNAL ARTICLE
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