Translation surfaces in Lie groups with constant Gaussian curvature

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.

arXiv commentarXiv admin note: text overlap with arXiv:2211.06577