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Symmetry 2018, 10(8), 317;

On Special Kinds of Involute and Evolute Curves in 4-Dimensional Minkowski Space

School of Mathematical Science, Dalian University of Technology, Dalian 116024, China
Department of Mathematics, Prince Sattam Bin Abdulaziz University, Alkharj 11991, Saudi Arabia
Author to whom correspondence should be addressed.
Received: 18 June 2018 / Revised: 6 July 2018 / Accepted: 22 July 2018 / Published: 2 August 2018
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Recently, extensive research has been done on evolute curves in Minkowski space-time. However, the special characteristics of curves demand advanced level observations that are lacking in existing well-known literature. In this study, a special kind of generalized evolute and involute curve is considered in four-dimensional Minkowski space. We consider (1,3)-evolute curves with respect to the casual characteristics of the (1,3)-normal plane that are spanned by the principal normal and the second binormal of the vector fields and the (0,2)-evolute curve that is spanned by the tangent and first binormal of the given curve. We restrict our investigation of (1,3)-evolute curves to the (1,3)-normal plane in four-dimensional Minkowski space. This research contribution obtains a necessary and sufficient condition for the curve possessing the generalized evolute as well as the involute curve. Furthermore, the Cartan null curve is also discussed in detail. View Full-Text
Keywords: evolute; involute curves; mate curves; minkowski space evolute; involute curves; mate curves; minkowski space
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).

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Hanif, M.; Hou, Z.H.; Nisar, K.S. On Special Kinds of Involute and Evolute Curves in 4-Dimensional Minkowski Space. Symmetry 2018, 10, 317.

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