Bulletin of the Korean Mathematical Society (대한수학회보)

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CANAL HYPERSURFACES GENERATED BY NON-NULL CURVES IN LORENTZ-MINKOWSKI 4-SPACE

  • Mustafa Altin (Technical Sciences Vocational School Bingol University) ;
  • Ahmet Kazan (Department of Computer Technologies Malatya Turgut Ozal University) ;
  • Dae Won Yoon (Department of Mathematics Education and RINS Gyeongsang National University)
  • Received : 2022.09.30
  • Accepted : 2023.05.31
  • Published : 2023.09.30
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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 hyper-cones whose centers lie on a non-null curve with non-null Frenet vector fields in E41 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 E41 by taking constant radius function and finally, we construct some examples and visualize them with the aid of Mathematica.

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Acknowledgement

The authors would like to gratefully thank the referee for the constructive comments and recommendations which definitely helped to improve the readability and quality of the paper.

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