Canal Hypersurfaces Generated by Pseudo Null, Partially Null and Null Curves in Lorentz-Minkowski 4-Space

TL;DR

This paper derives parametric equations and geometric properties of canal hypersurfaces generated by special curves in Lorentz-Minkowski 4-space, including examples and characterizations of tubular hypersurfaces.

Contribution

It provides explicit parametric forms and geometric invariants for canal hypersurfaces generated by pseudo null, partially null, and null curves in Lorentz-Minkowski 4-space, a novel extension in this geometric context.

Findings

Explicit parametric expressions for canal hypersurfaces.

Computed geometric invariants such as Gaussian and mean curvatures.

Characterizations of tubular hypersurfaces in Lorentz-Minkowski 4-space.

Abstract

In this paper, we obtain the parametric expressions of the canal hypersurfaces that are formed as the envelope of a family of pseudo hyperspheres or pseudo hyperbolic hyperspheres whose centers lie on a pseudo null, partially null or null curves in $E^4_1$ and give their some geometric invariants such as unit normal vector fields, Gaussian curvatures and mean curvatures. Also, we construct some examples for these canal hypersurfaces and finally, we give some characterizations for tubular hypersurfaces in $E^4_1$.