Meridian Surfaces with Parallel Normalized Mean Curvature Vector Field in Pseudo-Euclidean 4-space with Neutral Metric

Abstract

We construct a special class of Lorentz surfaces in the pseudo-Euclidean 4-space with neutral metric which are one-parameter systems of meridians of rotational hypersurfaces with timelike or spacelike axis and call them meridian surfaces. We give the complete classification of the meridian surfaces with parallel mean curvature vector field. We also classify the meridian surfaces with parallel normalized mean curvature vector. We show that in the family of the meridian surfaces there exist Lorentz surfaces which have parallel normalized mean curvature vector field but not parallel mean curvature vector.

15 pages. arXiv admin note: text overlap with arXiv:1606.00044

References in corpus (2)

• Invariants and bonnet-type theorem for surfaces in $\r^4$
• Submanifolds with parallel mean curvature vector in Riemannian and indefinite space forms

Cited by in corpus (1)

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