Meridian Surfaces on Rotational Hypersurfaces with Lightlike Axis in ${\mathbb E}^4_2$

摘要

We construct a special class of Lorentz surfaces in the pseudo-Euclidean4-space with neutral metric which are one-parameter systems of meridians ofrotational hypersurfaces with lightlike axis and call them meridian surfaces.We give the complete classification of the meridian surfaces with constantGauss curvature and prove that there are no meridian surfaces with parallelmean curvature vector field other than CMC surfaces lying in a hyperplane. Wealso classify the meridian surfaces with parallel normalized mean curvaturevector field. We show that in the family of the meridian surfaces there existLorentz surfaces which have parallel normalized mean curvature vector field butnot parallel mean curvature vector.