Harmonic Morphisms and Minimal Conformal Foliations on Lie Groups

IF 0.7 3区数学 Q3 MATHEMATICS

Annals of Global Analysis and Geometry Pub Date : 2025-08-30 DOI:10.1007/s10455-025-10015-2

Sigmundur Gudmundsson, Thomas Jack Munn

引用次数: 0

Abstract

Let G be a Lie group equipped with a left-invariant Riemannian metric. Let K be a semisimple and normal subgroup of G generating a left-invariant conformal foliation \(\mathcal {F}\) on G. We then show that the foliation \(\mathcal {F}\) is Riemannian and minimal. This means that locally the leaves of \(\mathcal {F}\) are fibres of a harmonic morphism. We also prove that if the metric restricted to K is biinvariant then \(\mathcal {F}\) is totally geodesic.

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李群上的调和态射与极小共形叶

设G是具有左不变黎曼度规的李群。设K是G的半简单正规子群，在G上产生一个左不变保形叶形\(\mathcal {F}\)，然后证明该叶形\(\mathcal {F}\)是黎曼极小的。这意味着\(\mathcal {F}\)的叶子在局部是谐波态射的纤维。我们也证明了如果限定于K的度规是双不变的，那么\(\mathcal {F}\)是完全测地线的。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Annals of Global Analysis and Geometry 数学-数学

CiteScore

1.20

自引率

0.00%

发文量

审稿时长

6-12 weeks

期刊介绍： This journal examines global problems of geometry and analysis as well as the interactions between these fields and their application to problems of theoretical physics. It contributes to an enlargement of the international exchange of research results in the field. The areas covered in Annals of Global Analysis and Geometry include: global analysis, differential geometry, complex manifolds and related results from complex analysis and algebraic geometry, Lie groups, Lie transformation groups and harmonic analysis, variational calculus, applications of differential geometry and global analysis to problems of theoretical physics.