Geometrical Properties of the Pseudonull Hypersurfaces in Semi-Euclidean 4-Space

Jianguo Sun,Xiaoyan Jiang,Fenghui Ji

doi:10.3390/math9111274

Abstract

In this paper, we focus on some geometrical properties of the partially null slant helices in semi-Euclidean 4-space. By structuring suitable height functions, we obtain the singularity types of the pseudonull hypersurfaces, which are generated by the partially null slant helices. An example is given to determine the main results.

Highlights

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We construct a special kind of null hypersurface along a partially null slant helix and obtain its singularity types, which can help scientists to further study the shape of the black hole horizon
We investigate the differential geometry and the singularity properties of the pseudonull hypersurfaces of the partially null slant helices in semi-Euclidean 4-space

Summary

Introduction

We construct a special kind of null hypersurface along a partially null slant helix and obtain its singularity types, which can help scientists to further study the shape of the black hole horizon. Starting from the singularity, in this paper, we study the singularity properties of the pseudonull hypersurfaces of the partially null slant helices in semi-Euclidean 4-space with index two using singularity theory. The first author [1,20] studied the singularity properties of some null curves in different spaces. We investigate the differential geometry and the singularity properties of the pseudonull hypersurfaces of the partially null slant helices in semi-Euclidean 4-space. We introduce the definition of the pseudonull hypersurface and obtains some geometrical properties of the partially null slant helices.

Preliminaries and the Main Results

The Height Function

The Proof of the Theorem 3

Example