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.
Mustafa Altın, Ahmet Kazan, Dae Won Yoon
Bing\"{o}l University; Malatya Turgut \"{O}zal University; Gyeongsang National University
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
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