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arXiv · 2211.06616

Translation surfaces in Lie groups with constant Gaussian curvature

Xu Han·Zhonghua Hou
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Abstract

Let G be a n-dimensional Lie group (n>2) 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 3-dimensional case.

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Xu Han, Zhonghua Hou. 2022-11-12. Translation surfaces in Lie groups with constant Gaussian curvature. https://arxiv.org/abs/2211.06616

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