Translation Surfaces in Lie Groups with Constant Gaussian Curvature

IF 0.4 3区数学 Q4 MATHEMATICS

Transformation Groups Pub Date : 2024-03-09 DOI:10.1007/s00031-024-09852-5

Xu Han, Zhonghua Hou

引用次数: 0

Abstract

Let G be an n-dimensional \((n\ge 3)\) Lie group with a bi-invariant Riemannian metric. We prove that if a surface of constant Gaussian curvature in G can be expressed as the product of two curves, then it must be flat. In particular, we can essentially characterize all such surfaces locally in the three-dimensional case.

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具有恒定高斯曲率的李群中的平移曲面

让 G 是一个 n 维（（n\ge 3）\)具有双不变黎曼度量的李群。我们证明，如果 G 中的恒定高斯曲率曲面可以表示为两条曲线的乘积，那么它一定是平坦的。特别是，在三维情况下，我们基本上可以描述所有此类曲面的局部特征。

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

Transformation Groups 数学-数学

CiteScore

1.60

自引率

0.00%

发文量

100

审稿时长

9 months

期刊介绍： Transformation Groups will only accept research articles containing new results, complete Proofs, and an abstract. Topics include: Lie groups and Lie algebras; Lie transformation groups and holomorphic transformation groups; Algebraic groups; Invariant theory; Geometry and topology of homogeneous spaces; Discrete subgroups of Lie groups; Quantum groups and enveloping algebras; Group aspects of conformal field theory; Kac-Moody groups and algebras; Lie supergroups and superalgebras.