English

Translation surfaces in Lie groups with constant Gaussian curvature

Differential Geometry 2023-08-07 v2

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.

Keywords

Cite

@article{arxiv.2211.06616,
  title  = {Translation surfaces in Lie groups with constant Gaussian curvature},
  author = {Xu Han and Zhonghua Hou},
  journal= {arXiv preprint arXiv:2211.06616},
  year   = {2023}
}

Comments

arXiv admin note: text overlap with arXiv:2211.06577