Meridian Surfaces of Parabolic Type in the Four-dimensional Minkowski Space

Abstract

We construct a special class of spacelike surfaces in the Minkowski 4-space which are one-parameter systems of meridians of the rotational hypersurface with lightlike axis and call these surfaces meridian surfaces of parabolic type. They are analogous to the meridian surfaces of elliptic or hyperbolic type. Using the invariants of these surfaces we give the complete classification of the meridian surfaces of parabolic type with constant Gauss curvature or constant mean curvature. We also classify the Chen meridian surfaces of parabolic type and the meridian surfaces of parabolic type with parallel normal bundle.