Canal Hypersurfaces Generated by Non-Null Curves with Parallel Frame in Minkowski Space-Time

TL;DR

This paper characterizes canal hypersurfaces generated by non-null curves with parallel frames in Minkowski space-time, providing formulas for curvatures and geometric invariants.

Contribution

It introduces new geometric characterizations and parametrizations of canal hypersurfaces formed by non-null curves with parallel frames in Minkowski space-time.

Findings

Derived formulas for Gaussian, mean, and principal curvatures.

Provided parametrizations of canal hypersurfaces in Minkowski space-time.

Identified geometric invariants and conditions for these hypersurfaces.

Abstract

In the present paper, firstly we obtain the canal hypersurfaces that are formed as the envelope of a family of pseudo hyperspheres or pseudo hyperbolic hyperspheres whose centers lie on a spacelike curve with parallel timelike normal vector field $B_{2}$ in Minkowski space-time and we give some geometric characterizations for them by obtaining the Gaussian curvature, mean curvature and principal curvatures of these canal hypersurfaces. Also, we give the general expression of parametrizations of the canal hypersurfaces generated by non-null curves with parallel frame in $E_{1}^{4}$ and we obtain some important geometric invariants and characterizations for them.