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

TL;DR

This paper introduces a new class of spacelike surfaces in four-dimensional Minkowski space, called meridian surfaces of parabolic type, and provides a complete classification based on curvature properties.

Contribution

It constructs and classifies meridian surfaces of parabolic type in Minkowski space, extending the understanding of such surfaces with constant curvature and special geometric properties.

Findings

Classified meridian surfaces of parabolic type with constant Gauss curvature.

Classified meridian surfaces of parabolic type with constant mean curvature.

Identified Chen meridian surfaces and those with parallel normal bundle.

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.