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