Constant curvature twisted surfaces in 3-dimensional Euclidean and Minkowski 3-space

A planar curve subject to two synchronized rotations, one in its supporting plane and one of this plane about some axis in the plane, possibly at different speeds, traces out what is called a twisted surface. From this construction, it is clear that surfaces of revolution are a special kind of twisted surfaces. We present here classifications of twisted surfaces that have constant Gaussian curvature or constant mean curvature in Euclidean and in Minkowski 3-space.