Bulletin of the
Korean Mathematical Society
BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

Article

HOME ALL ARTICLES View

Bull. Korean Math. Soc. 2023; 60(5): 1299-1320

Online first article September 11, 2023      Printed September 30, 2023

https://doi.org/10.4134/BKMS.b220680

Copyright © The Korean Mathematical Society.

Canal hypersurfaces generated by non-null curves in Lorentz-Minkowski 4-space

Mustafa Altın, Ahmet Kazan, Dae Won Yoon

Bing\"{o}l University; Malatya Turgut \"{O}zal University; Gyeongsang National University

Abstract

In the present paper, firstly we obtain the general expression of the canal hypersurfaces that are formed as the envelope of a family of pseudo hyperspheres, pseudo hyperbolic hyperspheres and null hypercones whose centers lie on a non-null curve with non-null Frenet vector fields 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.

Keywords: Canal hypersurface, tubular hypersurface, Lorentz-Minkowski 4-space, Weingarten hypersurface

MSC numbers: Primary 53A35, 53B30

Stats or Metrics

Share this article on :

Related articles in BKMS