Surfaces of constant Gauss curvature in Lorentz-Minkowski three-space

摘要

Let M be a space-like or time-like surface in Lorentz-Minkowski three-space L-3 generated by a one-parameter family of circular arcs. We show that if the Gauss curvature K is a nonzero constant, then M is a surface of revolution. We also describe the parametrizations for M when K drop 0. [References: 14]