Canal Hypersurfaces Generated by Non-Null Curves in Lorentz-Minkowski 4-Space

TL;DR

This paper derives the general formulas for canal hypersurfaces generated by non-null curves in Lorentz-Minkowski 4-space, exploring their geometric properties, flatness, minimality, and providing visualizations.

Contribution

It introduces new explicit expressions and characterizations for canal hypersurfaces in Lorentz-Minkowski space, including invariants and special conditions.

Findings

Derived formulas for geometric invariants of canal hypersurfaces.

Identified conditions for flatness and minimality.

Constructed and visualized specific examples.

Abstract

In the present paper, firstly we obtain the general expression of the canal hypersurfaces which are formed as the envelope of a family of pseudo hyperspheres, pseudo hyperbolic hyperspheres and null hypercones in $E_{1}^{4}$ and give their some geometric invariants such as unit normal vector fields, Gaussian curvatures, mean curvatures and principal curvatures. Also we give some results about their flatness and minimality conditions and Weingarten canal hypersurfaces. Also, we obtain these characterizations for tubular hypersurfaces in $E_{1}^{4}$ by taking constant radius function and finally we construct some examples and visualize them with the aid of Mathematica.