具有恒定高斯曲率的李群中的平移曲面

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

Xu Han, Zhonghua Hou

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引用次数: 0

摘要

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。

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Translation Surfaces in Lie Groups with Constant Gaussian Curvature

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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