On Special Kinds of Involute and Evolute Curves in 4-Dimensional Minkowski Space
AbstractRecently, 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
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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.
Hanif M, Hou ZH, Nisar KS. On Special Kinds of Involute and Evolute Curves in 4-Dimensional Minkowski Space. Symmetry. 2018; 10(8):317.Chicago/Turabian Style
Hanif, Muhammad; Hou, Zhong H.; Nisar, Kottakkaran S. 2018. "On Special Kinds of Involute and Evolute Curves in 4-Dimensional Minkowski Space." Symmetry 10, no. 8: 317.
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